Journal articles on the topic 'Vacua configuration'

We study vacuum fluctuation properties of an ensemble of S U ( N ) gauge theory configurations, in the limit of many colors, viz. N c → ∞ , and explore the statistical nature of the topological susceptibility by analyzing its critical behavior at a non-zero-vacuum parameter θ and temperature T. We find that the system undergoes a vacuum phase transition at the chiral symmetry restoration temperature as well as at an absolute value of θ . On the other hand, the long-range correlation length solely depends on θ for the theories with critical exponent e = 2 or T = T d + 1 , where T d is the decoherence temperature. Furthermore, it is worth noticing that the unit-critical exponent vacuum configuration corresponds to a non-interacting statistical basis pertaining to a constant mass of η ′ .

The type IIA nonsupersymmetric meta-stable brane configuration consisting of three NS5-branes, D4-branes and anti-D4-branes where the electric gauge theory superpotential has a quartic term for the bifundamentals besides a mass term is constructed. By adding the orientifold 4-plane and 6-plane to this brane configuration, we also describe the intersecting brane configurations of type IIA string theory corresponding to the meta-stable nonsupersymmetric vacua of corresponding gauge theories.

It has not been clarified whether a matrix model can describe various vacua of string theory. In this talk, we show that the IIB matrix model includes type IIA string theory1. In the naive large N limit of the IIB matrix model, configurations consisting of simultaneously diagonalizable matrices form a moduli space, although the unique vacuum would be determined by complicated dynamics. This moduli space should correspond to a part of perturbatively stable vacua of string theory. Actually, one point on the moduli space represents type IIA string theory. Instead of integrating over the moduli space in the path-integral, we can consider each of the simultaneously diagonalizable configurations as a background and set the fluctuations of the diagonal elements to zero. Such procedure is known as quenching in the context of the large N reduced models. By quenching the diagonal elements of the matrices to an appropriate configuration, we show that the quenched IIB matrix model is equivalent to the two-dimensional large N [Formula: see text] super Yang-Mills theory on a cylinder. This theory is nothing but matrix string theory and is known to be equivalent to type IIA string theory. As a result, we find the manner to take the large N limit in the IIB matrix model.

We consider free massive matter fields in static scalar, electric and gravitational backgrounds. Tuning these backgrounds to the brink of vacuum decay, we identify a term in their effective action that is singular. This singular term is universal, being independent of the features of the background configuration. In the case of gravitational backgrounds, it can be interpreted as a quantum mechanical analog of Choptuik scaling. If the background is tuned slightly above the instability threshold, this singular term gives the leading contribution to the vacuum decay rate. Dedicated to the memory of Ludwig Faddeev

We construct the type IIA nonsupersymmetric meta-stable brane configuration consisting of (2k+1) NS5-branes and D4-branes where the electric gauge theory superpotential has an order (2k+2) polynomial for the bifundamentals. We find a rich pattern of nonsupersymmetric meta-stable states as well as the supersymmetric stable ones. By adding the orientifold 4-plane to this brane configuration, we also describe the intersecting brane configuration of type IIA string theory corresponding to the meta-stable nonsupersymmetric vacua of corresponding gauge theory.

Starting from an [Formula: see text] supersymmetric electric gauge theory with the gauge group Sp (N c ) × SO (2N′ c ) with fundamentals for the first gauge group factor and a bifundamental, we apply Seiberg dual to the symplectic gauge group only and arrive at the [Formula: see text] supersymmetric dual magnetic gauge theory with dual matters including the gauge singlets and superpotential. By analyzing the F-term equations of the dual magnetic superpotential, we describe the intersecting brane configuration of type IIA string theory corresponding to the meta-stable nonsupersymmetric vacua of this gauge theory.

We present the scalar moduli stabilization from the perspective of the real intrinsic geometry. In this paper, we describe the physical nature of the vacuum moduli fluctuations of an arbitrary Fayet configuration. For finitely many Abelian scalar fields, we show that the framework of the real intrinsic geometry investigates the mixing between the marginal and threshold vacua. Interestingly, we find that the phenomena of wall crossing and the search of the stable vacuum configurations, pertaining to D-term and F-term scalar moduli, can be accomplished for the Abelian charges. For given vacuum expectation values of the moduli scalars, we provide phenomenological aspects of the vacuum fluctuations and phase transitions in the supersymmetry breaking configurations.

In a general superstring vacuum configuration, the “internal” space (sector) varies in space-time. When this variation is nontrivial only in two spacelike dimensions, the vacuum contains static cosmic strings with finite energy per unit length and which is, up to interactions with matter, an easily computed topological invariant. The total space-time is smooth although the “internal” space is singular at the center of each cosmic string. In a similar analysis of the Wick-rotated Euclidean model, these cosmic strings acquire expected self-interactions. Also, a possibility emerges to define a global time in order to rotate back to the Lorentzian case.

We report the first application of a recently proposed regularization procedure for multi-reference energy density functionals, which removes spurious divergent or non-continuous contributions to the binding energy, to a general configuration mixing. As an example, we present a calculation that corresponds to the particle-number and angular momentum projection of axially symmetric time-reversal invariant quasiparticle vacua of different quadrupole deformation for the nucleus 18 O . The SIII parameterization of the Skyrme energy functional is used.

Starting from an [Formula: see text] supersymmetric electric gauge theory with the multiple product gauge group and the bifundamentals, we apply Seiberg dual to each gauge group, obtain the [Formula: see text] supersymmetric dual magnetic gauge theories with dual matters including the gauge singlets. Then we describe the intersecting brane configurations, where there are NS-branes and D4-branes (and anti-D4-branes), of type IIA string theory corresponding to the meta-stable nonsupersymmetric vacua of this gauge theory. We also discuss the case where the orientifold 4-planes are added into the above brane configuration. Next, by adding an orientifold 6-plane, we apply to an [Formula: see text] supersymmetric electric gauge theory with the multiple product gauge group (where a single symplectic or orthogonal gauge group is present) and the bifundamentals. Finally, we describe the other cases where the orientifold 6-plane intersects with NS-brane.

I propose a new mechanism to account for the observed tiny but finite dark energy in terms of a non-Abelian Higgs theory, which has infinitely many perturbative vacua characterized by a winding number, in the framework of inflationary cosmology. Inflation homogenizes field configuration and practically realizes a perturbative vacuum with vanishing winding number, which is expressed by a superposition of eigenstates of the Hamiltonian with different vacuum energy density. As a result, we naturally find a nonvanishing vacuum energy density with fairly large probability, under the assumption that the cosmological constant vanishes in some vacuum state. Since the predicted magnitude of dark energy is exponentially suppressed by the instanton action, we can fit observation without introducing any tiny parameters.

Quantum chromodynamics is a fundamental non-Abelian gauge theory of strong interactions. The physical quantum chromodynamics vacuum state is a linear superposition of the [Formula: see text]-vacua states with different topological numbers. Because of the configuration of the gauge fields, the tunneling events can induce the local parity-odd domains. Those interactions that occur in these domains can be affected by these effects. Considering the hadron (nucleon) system, we introduce the parity-odd parton distribution functions in order to describe the parity-odd structures inside the hadron in this paper. We obtain 8 parity-odd parton distribution functions at leading twist for spin-1/2 hadrons and present their properties. By introducing the parity-odd quark–quark correlator, we find the parity-odd effects vanish from the macroscopic point of view. In this paper, we consider the high energy semi-inclusive deeply inelastic scattering process to investigate parity-odd effects by calculating the spin asymmetries.

We present a formulation of the stationary bosonic string sector of the whole toroidally compactified effective field theory of the heterotic string as a double Ernst system which, in the framework of general relativity describes, in particular, a pair of interacting spinning black holes; however, in the framework of low-energy string theory the double Ernst system can in particular be interpreted as the rotating field configuration of two interacting sources of black hole type coupled to dilaton and Kalb–Ramond fields. We clarify the rotating character of the Btφ-component of the antisymmetric tensor field of Kalb–Ramond and discuss on its possible torsion nature. We also recall the fact that the double Ernst system possesses a discrete symmetry which is used to relate physically different string vacua. Therefore we apply the normalized Harrison transformation (a charging symmetry which acts on the target space of the low-energy heterotic string theory preserving the asymptotics of the transformed fields and endowing them with multiple electromagnetic charges) on a generic solution of the double Ernst system and compute the generated field configurations for the 4-D effective field theory of the heterotic string. This transformation generates the U (1)n vector field content of the whole low-energy heterotic string spectrum and gives rise to a pair of interacting rotating black holes endowed with dilaton, Kalb–Ramond and multiple electromagnetic fields where the charge vectors are orthogonal to each other.

Abstract The Logarithmic Linear Relaxation (LLR) algorithm is an efficient method for computing densities of states for systems with a continuous spectrum. A key feature of this method is exponential error reduction, which allows us to evaluate the density of states of a system over hundreds of thousands of orders of magnitude with a fixed level of relative accuracy. As a consequence of exponential error reduction, the LLR method provides a robust alternative to traditional Monte Carlo calculations in cases in which states suppressed by the Boltzmann weight play nevertheless a relevant role, e.g., as transition regions between dominant configuration sets. After reviewing the algorithm, we will show an application in U(1) Lattice Gauge Theory that has enabled us to obtain the most accurate estimate of the critical coupling with modest computational resources, defeating exponential tunneling times between metastable vacua. As a further showcase, we will then present an application of the LLR method to the decorrelation of the topological charge in SU(3) Lattice Gauge Theory near the continuum limit. Finally, we will review in general applications of the LLR algorithm to systems affected by a strong sign problem and discuss the case of the Bose gas at finite chemical potential.

The purpose of this paper is to investigate the quantum vacua directly implied by the wave function of a gravitational configuration characterized by the presence of an apparent horizon, namely the Vaidya space–time solution. Spherical symmetry is a main feature of this configuration, with a scalar field constituting a source [a Klein–Gordon geon or Berger–Chitre–Moncrief–Nutku (BCMN) type model]. The subsequent analysis requires solving a Wheeler–DeWitt equation near the apparent horizon (following the guidelinesintroduced by A. Tomimatsu,18; M. Pollock,19 and developed by A. Hosoya and I. Oda20,21) with the scalar field herein expanded in terms of S2 spherical harmonics: midisuperspace quantization. The main results present in this paper are as follows. It is found that the mass function characteristic of the Vaidya metric is positive definite within this quantum approach. Furthermore, the inhomogeneous matter sector determines a descrip-tion in terms of open quantum (sub)systems, namely in the form of an harmonic oscillator whose frequency depends on the mass function. For this open (sub)system, a twofold approach is employed. On the one hand, an exact invariant observable is obtained from the effective Hamiltonian for the inhomogeneous matter modes. It is shown that this invariant admits a set of discrete eigenvalues which depend on the mass function. The corresponding set of eigenstates is constructed from a particular vacuum state. On the other hand, exact solutions are found for the Schrädinger equation associated with the inhomogeneous matter modes. This paper is concluded with a discussion, where two other issues are raised: (i) the possible application to realistic black hole dynamics of the results obtained for a simplified (BCMN) model and (ii) whether such vacuum states could be related with others defined instead within scalar field theories constructed in classical backgrounds.

We first give a proof that the supersymmetric configurations satisfy the equations of motion for type II supergravity. In flux compactifications, the string vacua preserving N = 2 supersymmetry are the twisted generalized Calabi–Yau manifold. The modulus space of the string vacua can be constructed. We discuss the generalized Dirac operator which adds a torsional term to the ordinary Dirac operator and compute its index by the path integral method. Via the variation of the action of supergravity one can introduce the generalized Ricci flow equations. We consider deforming the manifold with the generalized Ricci flow. Finally, we consider the linear stability of the fixed points of the generalized Ricci flow.

From an [Formula: see text] supersymmetric electric gauge theory with the gauge group SU (Nc) × SU (N′c) with fundamentals for each gauge group, the bifundamentals and a symmetric flavor and a conjugate symmetric flavor for SU (Nc), we apply Seiberg dual to each gauge group independently and obtain two [Formula: see text] supersymmetric dual magnetic gauge theories with dual matters including the gauge singlets. By analyzing the F-term equations of the dual magnetic superpotentials, we describe the intersecting brane configurations of type IIA string theory corresponding to the meta-stable nonsupersymmetric vacua of these gauge theories. The case where the above symmetric flavor is replaced by an antisymmetric flavor is also discussed.

We study configurations of intersecting domain walls in a Wess–Zumino model with three vacua. We introduce a volume-preserving flow and show that its static solutions are configurations of intersecting domain walls that form double bubbles, that is, minimal area surfaces which enclose and separate two prescribed volumes. To illustrate this field theory approach to double bubbles, we use domain walls to reconstruct the phase diagram for double bubbles in the flat square two-torus and also construct all known examples of double bubbles in the flat cubic three-torus.

From an [Formula: see text] supersymmetric electric gauge theory with the gauge group [Formula: see text] with fundamentals for each gauge group and the bifundamentals, we apply Seiberg dual to each gauge group and obtain the [Formula: see text] supersymmetric dual magnetic gauge theories with dual matters including the additional gauge singlets. By analyzing the F-term equations of the dual magnetic superpotentials, we describe the intersecting brane configurations of type IIA string theory corresponding to the meta-stable nonsupersymmetric vacua of this gauge theory. We apply also to the case for [Formula: see text] supersymmetric electric gauge theory with the gauge group [Formula: see text] with flavors for each gauge group and the bifundamentals. Finally, we describe the meta-stable brane configurations of multiple product gauge groups.

Molecular mechanics and dynamics simulations were carried out to study the capacity of isoleucine enantiomers to form inclusion complexes with β–cyclodextrin, and to be discriminated by this chiral compound, in vacuo and with different solvents. Solvents were characterized not only by the value of dielectric constant ε in the Coulombic interaction energy, but also by the neutral and zwitterion configurations of isoleucine. Whereas the discrimination between the enantiomers for ε ≤ 2 is due to the electrostatic contribution, these differences are mainly due to the Lennard-Jones potential for ε > 2. The most enantioselective regions are located near the cavity walls, independently of the solvent. D-Ile is more stable than L-Ile in broader regions in vacuo, but L-Ile presents more stable locations with water. Isoleucine can form inclusion complexes with β–cyclodextrin in vacuo and with different solvents. Two probable configurations are deduced from the molecular dynamics simulation, in which the guest is always inside the cavity and with the carboxylic end of the amino acid oriented towards either rim of β–CD. In the simulation, the enantiomers preferentially occupy regions with greater chiral discrimination. The first eluted enantiomer in vacuo and with different solvents is L-Ile, independently of the solvent polarity.

We study the dynamics of D-branes in the near-horizon geometry of NS fivebranes. This leads to a holographically dual description of the physics of D-branes ending on and/or intersecting NS5-branes. We use it to verify some properties of such D-branes which were deduced indirectly in the past, and discuss some instabilities of non-supersymmetric brane configurations. Our construction also describes vacua of Little String Theory which are dual to open plus closed string theory in asymptotically linear dilaton spacetimes.

In the present paper, we investigated the gravitational black-hole-hedgehog’s solution with magnetic field contribution in the framework of the [Formula: see text]-gravity described by the Gravi-weak unification (GWU) model. Assuming the Multiple Point Principle (MPP), we considered the existence of the two degenerate vacua of the Universe: the first Electroweak (EW)-vacuum with [Formula: see text] GeV (“true vacuum”), and the second Planck scale (“false vacuum”) with [Formula: see text] GeV. In these vacua, we investigated different topological defects. The main aim of this paper is an investigation of the black-hole-hedgehog configurations as defects of the “false vacuum.” We have obtained the solution which corresponds to a global monopole, that has been “swallowed” by the black-hole with core mass [Formula: see text] GeV and radius [Formula: see text] GeV[Formula: see text]. We investigated the metric in the vicinity of the black-hole-hedgehog and estimated its horizon radius: [Formula: see text]. We have considered the phase transition from the “false vacuum” to the “true vacuum” and confirmed the stability of the EW-vacuum.

We find a background solution of the string theory which has a special property distinguished from the usual background solutions. This background solution does not produce the NS-NS two-form fields under T-duality and therefore the background vacua described by this solution essentially do not involve NS-NS type branes in their configurations, unlike the case of the ordinary Calabi–Yau ansatz. As a result the non-linear [Formula: see text]-models, whose target space metrics are given by these T-dual partners, can both be torsion-free.

Abstract Some false vacua do not decay via bounces. This usually happens when a flat direction of the tunneling action due to scale invariance is lifted to a sloping valley by a scale breaking perturbation, pushing the bounce off to infinity. We compare two types of alternative decay configurations that have been proposed recently to describe decay in such cases: pseudo-bounces and new instantons. Although both field configurations are quite similar, we find that the pseudo-bounce action is lower than the new instanton one and describes more faithfully the bottom of the action valley. In addition, pseudo-bounces cover a range of field space wider than new instantons and, as a result, lead to a decay rate that can be lower than the one via new instantons by orders of magnitude.

Starting from an [Formula: see text] supersymmetric electric gauge theory with the gauge group [Formula: see text] with fundamentals for each gauge group, the bifundamentals, a symmetric flavor and a conjugate symmetric flavor for SU (Nc), we apply Seiberg dual to each gauge group, obtain the [Formula: see text] supersymmetric dual magnetic gauge theories with dual matters including the gauge singlets, and describe the intersecting brane configurations of type IIA string theory corresponding to the meta-stable nonsupersymmetric vacua of this gauge theory. We also discuss the case where a symmetric flavor is replaced by an antisymmetric flavor. Next we apply to the case for [Formula: see text] supersymmetric electric gauge theory with the gauge group [Formula: see text] with flavors for each gauge group and the bifundamentals. Finally, we describe the case where the orientifold 6-plane charge is reversed.

In the present paper, assuming the Multiple Point Principle (MPP) as a new law of Nature, we considered the existence of the two degenerate vacua of the Universe: the first Electroweak (EW) vacuum at [Formula: see text][Formula: see text]GeV — “true vacuum”, and the second Planck scale “false vacuum” at [Formula: see text] GeV. In these vacua, we investigated different topological defects. The main aim of this paper is an investigation of the black-hole-hedgehogs configurations as defects of the false vacuum. In the framework of the [Formula: see text] gravity, described by the Gravi-Weak unification model, we considered a black-hole solution, which corresponds to a “hedgehog” — global monopole, that has been “swallowed” by the black-hole with mass core [Formula: see text][Formula: see text]GeV and radius [Formula: see text][Formula: see text]GeV[Formula: see text]. Considering the results of the hedgehog lattice theory in the framework of the [Formula: see text] Yang–Mills gauge-invariant theory with hedgehogs in the Wilson loops, we have used the critical value of temperature for the hedgehogs confinement phase ([Formula: see text][Formula: see text]GeV). This result gave us the possibility to conclude that the SM shows a new physics with contributions of the [Formula: see text]-triplet Higgs bosons at the scale [Formula: see text][Formula: see text]TeV. Theory predicts the stability of the EW-vacuum and the accuracy of the MPP.

Assuming the Multiple Point Principle (MPP) as a new law of Nature, we considered the existence of the two degenerate vacua of the Universe: (a) the first Electroweak (EW) vacuum at v 1 ≈ 246 GeV—“true vacuum”, and (b) the second Planck scale “false vacuum” at v 2 ∼ 10 18 GeV. In these vacua, we investigated different topological defects. The main aim of the paper is an investigation of the black-hole-hedgehogs configurations as defects of the false vacuum. In the framework of the f ( R ) gravity, described by the Gravi-Weak unification model, we considered a black-hole solution, which corresponds to a “hedgehog”—global monopole, that has been “swallowed” by the black-hole with mass core M B H ∼ 10 18 GeV and radius δ ∼ 10 − 21 GeV − 1 . Considering the results of the hedgehog lattice theory in the framework of the S U ( 2 ) Yang-Mills gauge-invariant theory with hedgehogs in the Wilson loops, we have used the critical value of temperature for the hedgehogs’ confinement phase ( T c ∼ 10 18 GeV). This result gave us the possibility to conclude that the SM shows a new physics (with contributions of the S U ( 2 ) -triplet Higgs bosons) at the scale ∼10 TeV. This theory predicts the stability of the EW-vacuum and the accuracy of the MPP.

We show how consistent quantization determines the renormalization of couplings in a quantum field theory coupled to gravity in two dimensions. The special status of couplings corresponding to conformally invariant matter is discussed. In string theory, where the dynamical degree of freedom of the two-dimensional metric plays the role of time in target space, these renormalization group equations are themselves the classical equations of motion. Time independent solutions, like classical vacuua, correspond to the situation in which matter is conformally invariant. Time dependent solutions, like tunnelling configurations between vacuua, correspond to special trajectories in theory space. We discuss an example of such a trajectory in the space containing the c < 1 minimal models. We also discuss the connection between this work and the recent attempts to construct non-perturbative string theories based on matrix models.

We have thoroughly analyzed the electronic structure of stacked DNA Watson–Crick (WC) base pair dimers using ab initio Hartree–Fock and semiempirical Hartree–Fock-configuration-interaction quantum chemistry. We consider all the possible base compositions and sequences at the nucleoside level in vacuo. The results show that in such systems charge carrier generation could in principle be possible via charge transfer excitons, which turn out to dominate the first excited electronic states of the WC base pairs and their stacked dimers, and this process is largely sequence- and conformation-dependent. Possible consequences of this result for polymeric DNA duplexes are discussed.

The standard electroweak model with Dirac neutrinos is extended by way of the principles of electroweak quark–lepton symmetry and weak topological-charge confinement to account for quark–lepton charge relations which, if not accidental, are indicative of charge structures. A mixing in quarks and leptons of underlying integer local charges with integer weak topological charges associated with an additive group Z3, fixed by the anomaly cancellation requirement, is discussed. It is found that the electroweak difference between topological quarks and leptons is the nonequivalence between the topological vacua of their weak field configurations, produced by a four-instanton which carries the topological charge, induces the universal fractional piece of charge distinguishing quarks from leptons, and breaks the underlying symmetry. The constituent quarks of the standard model appear as coming from topological quarks, via the weak four-instanton event. Dual transitions occur for leptons. It is shown that several other fundamental problems left open in the standard electroweak model with Dirac neutrinos are solved: the one-to-one correspondence between quark and lepton flavors, the existence of three generations, the conservation and ungauging of B-L, the electric charge quantization, and the confinement of fractional electric charges.

AbstractValidation of a linear numerical model of wave interactions with floating compliant discs is sought using data obtained from the wave basin experiments reported in Part 1 (Montiel et al. J. Fluid Mech., vol. 723, 2013, pp. 604–628). Comparisons are made for both single-disc tests and the two-disc tests in which wave interactions between discs are observed. The deflection of the disc or discs is separated into the natural modes of vibration in vacuo. The decomposition allows the rigid-body motions and flexural motions to be analysed separately. Rigid-body motions are accurately replicated by the numerical model but, although passable agreement is found, the amplitudes of flexural modes are consistently overestimated. Extensions of the numerical model are used to discount the experimental configuration as a source of the discrepancies. An enhanced viscoelastic model for the discs is also proposed, which results in improved model/data agreement for the flexural motions but cannot account for all of the disagreement.

String/M theory is formulated in 10 and 11 space-time dimensions; in order to describe our universe, we must postulate that six or seven of the spatial dimensions form a small compact manifold. In 1985, Candelas et al. showed that by taking the extra dimensions to be a Calabi–Yau manifold, one could obtain the grand unified theories which had previously been postulated as extensions of the Standard Model of particle physics. Over the years since, many more such compactifications were found. In the early 2000s, progress in nonperturbative string theory enabled computing the approximate effective potential for many compactifications, and it was found that they have metastable local minima with small cosmological constant. Thus, string/M theory appears to have many vacuum configurations which could describe our universe. By combining results on these vacua with a measure factor derived using the theory of eternal inflation, one gets a theoretical framework which realizes earlier ideas about the multiverse, including the anthropic solution to the cosmological constant problem. We review these arguments and some of the criticisms, with their implications for the prediction of low energy supersymmetry and hidden matter sectors, as well as recent work on a variation on eternal inflation theory motivated by computational complexity considerations.

This work considers the elastodynamic response of a rectangular plate supported by a fluid on one side, and subjected to impact loading on the other side. The presence of the fluid in our problem has the effect, first, of lowering the natural frequency of the plate due to the increased inertia, and secondly, of damping its vibrations owing to the energy carried off in the form of sound waves. The deflection of the plate is approximated by a double infinite series in the spatial coordinates. Each term of the series consists of a product of two modes of deflection of beams, having the same boundary conditions as the plate, multiplied by a time dependent function. The problem is solved for various combinations of fluids, impact loadings, geometrical configurations, and boundary conditions. Excellent agreement is obtained between the present results for eigen frequencies and the static deflections in vacuo and published results. Furthermore, good agreement is obtained for the added-mass and the damping magnitude. As for the dynamic case, since no complete solutions are available, the present results are at least shown to be self-consistent.

The crystal structures of eight cyclodipeptides are determined, incorporating pipecolic acid or proline and phenylalanine or N-methyl phenylalanine. This set of structures allows the evaluation of the effects on molecular conformation and crystal packing of imino acid ring-size, relative configuration of the two amino acids, and N-methylation. In the non-methylated compounds, hydrogen-bonding interactions form one-dimensional motifs that dominate the packing arrangement. Three compounds have more than one symmetry-independent molecule in the asymmetric unit (Z′ > 1), indicative of a broad and shallow molecular energy minimum. Density functional theory calculations reveal the interplay between inter- and intramolecular factors in the crystals. Only for the N-methylated compounds do simulations of the molecules in the isolated state succeed to reproduce the observed crystallographic conformations. Puckering of the diketopiperazine ring and the deviation from planarity of the amide bonds are not reproduced in the remaining compounds. Cluster in vacuo calculations with a central cyclodipeptide molecule surrounded by hydrogen-bound molecules establish that hydrogen bonding is of major importance but that other intermolecular interactions must also contribute substantially to the crystal structure. More advanced periodic calculations, incorporating the crystallographic environment to the full extent, are necessary to correctly describe all the conformational features of these cyclodipeptide crystals.

Abstract A series of six new single crystals of fully stoichiometric As3+-bearing Mo-oxides and partially W-substituted Mo-oxides with formula AsmO(Mo1−xWxO3)p (m = 1, 2; p = 5, 7, 9, 10 and 11 and 0 ≤ x ≤ 0.6) was successfully grown using vapor-phase transport in vacuo. The crystal structures were determined using single-crystal X-ray diffraction data. All these compounds exhibit acentric orthorhombic symmetry with Z = 2, and belong to the so-called (n)-ITB (intergrowth tungsten bronzes) family, with n = 2, 3, 4 and 5. The six (n)-ITB phases have the following formulae: (2)-AsMo5O16 (Pm 2a), (2)-As2Mo10O31 (Pma 2), (3)-AsMo7O22 (Pmn 21), (3)-As(Mo5.53W1.47)O22 (Pmn 21), (4)-As(Mo4.33W4.67)O28 (Pm 2a) and (5)-As(W6.63Mo4.37)O34 (Pmn 21). Their structures consist of vertex-sharing MO6 octahedral units (with M either Mo or Mo/W) connected so as to form three-dimensional frameworks. Such frameworks consist of perovskite tungsten bronzes (PTB) type slabs, from 2- to 5-octahedra wide, intergrown with single hexagonal tungsten bronzes (HTB) type slabs, stacked up to form pseudo-hexagonal tunnels along the a-axis. As3+ and additional oxygen atoms are located in off-center positions inside the tunnels, forming As–O bonds with peculiar arrangements. In particular, we obtained the first examples of structures where, besides the usual AsO3E distorted pyramidal geometry, As3+ adopts AsO4E coordination with a seesaw configuration.

Using geostatistical models of density variations in the subsurface, constrained by geologic data, forward models of gravity anomalies can be generated by discretizing the subsurface and calculating the cumulative effect of each cell (pixel). The results of such stochastically generated forward gravity anomalies can be compared with the observed gravity anomalies to find density models that match the observed data. These models have an advantage over forward gravity anomalies generated using polygonal bodies of homogeneous density because generating numerous realizations explores a larger region of the solution space. The stochastic modeling can be thought of as dividing the forward model into two components: that due to the shape of each geologic unit and that due to the heterogeneous distribution of density within each geologic unit. The modeling demonstrates that the internally heterogeneous distribution of density within each geologic unit can contribute significantly to the resulting calculated forward gravity anomaly. Furthermore, the stochastic models match observed statistical properties of geologic units, the solution space is more broadly explored by producing a suite of successful models, and the likelihood of a particular conceptual geologic model can be compared. The Vaca Fault near Travis Air Force Base, California, can be successfully modeled as a normal or strike-slip fault, with the normal fault model being slightly more probable. It can also be modeled as a reverse fault, although this structural geologic configuration is highly unlikely given the realizations we explored.

Ab initio computations (B3LYP/6-31G(D)) were used to predict transition structures and energies of activation for intramolecular H atom transfer to a thiyl radical (RS.) from the α-C—H bonds of glutathione (1) and from the model compounds, N-formylcysteinylglycine (2) and N-(2-thioethanyl)-γ-glutamine (3). For each compound, transition structures were located by in vacuo calculations on the neutral non-zwitterionic system. Thermodynamic functions derived at the same level and single point calculations at the B3LYP/6-311+G(3df,2p) level, were used to derive free energies of activation (ΔG[Formula: see text]) and reaction (ΔG°). For abstraction of the α-C—H (Gly) by the thiyl radical in the gas phase, ΔG[Formula: see text] = 134 kJ mol–1 if the amide link to Gly is in the more stable (Z)-configuration, and ΔG[Formula: see text] = 52 kJ mol–1 if it is in the less stable (E)-configuration. The isomerization of the amide group requires about 95 kJ mol–1. Previous studies had indicated that for intramolecular reaction of the thiyl radical at α-C—H (Cys), ΔG[Formula: see text] = 110 kJ mol–1. The lowest energy pathway for intramolecular H-transfer to the thiyl radical is from α-C—H (Gln), ΔG[Formula: see text] = 37–42 kJ mol–1, and corresponds rather well with experimental results in solution (ΔG[Formula: see text] = 43 kJ mol–1). The calculated free energy change for the equilibrium between thiyl and α-C forms of the glutathione radical is ΔG° = –54 kJ mol–1. The value estimated from experimental data is ΔG° = –37 kJ mol–1. The agreement between the energies from theory in the gas phase and experiment in solution suggests that the free energies of solvation of reactant thiyl radical, transition structures for H abstraction, and the product α-C-centred radical, are very similar. The effects of solution were estimated by two continuum models (SCIPCM and COSMO). The SCIPCM model yields results very similar to the gas phase, predicting a modest lowering of the activation free energy. The results from the COSMO method were inconclusive as to whether a rate enhancement or decrease could be expected.Key words: glutathione, thiyl radical, α-C-radical, hydrogen transfer.

Holding time is used for optimizing the bond diffusion between aluminum Al and Carbon steel SS400. The objective of this research was to investigate the effects of holding time on the interface reactions of diffusion welding between aluminum and carbon steel. Holding time variations of 10, 15, 30 and 45 minutes were applied at 950°C using mixture of Cu and Fe powder as elements promoter. Single lap joint configuration was performed in vacum furnace to join the dissimilar materials which allowed bonding diffusion. Microstructure was examined on the same test piece. It was found that during diffusion process at 950°C, the interfacial zone between aluminum and carbon steel substrate features intermetallic layers. The intermetallic thickness increased with increasing the holding time. Crack or incomplete bonding appeared on the specimens with holding time up to 30 minutes and didn’t appear on the specimens with holding time of 45 minutes. Cu rich-element promoter made diffusion penetrated deeper than Fe rich-element promoter in the same holding time. Macrostructure, microstructure and SEM examinations revealed that Al-steel joint had the best result with element promoter content of 60/40 % at 45 minutes holding time. There was no interlayer gap at this specimen. Additionally, from mapping view it can be suggested that in terms of poor interface bonding, Cu molecules were located just around the interface area, on the other hand, in case of strong interface bonding, Cu molecules are scattered throughout the specimen. In fact, the position of Cu molecules can be used as a promising marker for the detection of quality of diffusion joint.

Out of several plausible isomeric structures of the toluene–ICl charge transfer (CT) complex, the most feasible one was determined by a detailed ab initio and DFT study at the HF, B3LYP, and mPW1PW91 levels using 6-31++G(d, p) basis set. Potential energy surface scans were performed with six possible structures ( I and Cl facing the o-, m-, and p-carbon atoms of toluene separately); the structures at the local minima of the surfaces were subjected to frequency calculation and the ones having no negative frequency were accepted as the real structure in the ground state. These structures were then subjected to full optimization. It was observed that the I – Cl bond, with its I atom oriented toward the aromatic ring, stands vertically above a C -atom at the ortho or para positions, being inclined at about 9° to the line perpendicular to the aromatic ring. Complexation increases the I – Cl bond length. After correction for basis set superposition error through a counterpoise calculation, we conclude from the binding energy that the preferred structure is the one with ICl above the ortho C atom. The calculated binding energy closely matches the experimental free energy of complexation. The electronic CT transition energy (hν CT ) with this structure in the ground state was calculated in vacuo by the restricted configuration interaction singlets method and in carbontetrachloride medium by the time dependent density functional theory method under the polarizable continuum model. The value of hν CT obtained from the ground-to-excited state transition electric dipole moments of the complex, is close to (somewhat underestimated) the reported experimental value.

V. Rama Subbaraoa* aNatural Products Laboratory, Organic Chemistry Division-I, Indian Institute of Chemical Technology, Habsiguda, Hyderabad 500007, India. Study and optimization of Diels-Alder reaction of piperine in aqueous ionic solutions using Gn.HCl as a catalyst. The semi-synthesis of these products using intermolecular [4+2] cycloaddition reaction has been described. Obtained products were characterized using IR, HNMR, CNMR and Mass Spectroscopy. Introduction An outsized number of phenomena concern to and are conducted in liquid phase involving ionic species (Millions of years ago, Mother Nature discovered the secrets of water molecule) in different biological and other natural processes. Salt present in the oceans, a striking example from Nature, is a multi component salt solution reflecting the distant marine origin of life on earth together with the composition of physiological fluids. In general the ionic solutions play roles in several industrial and geological processes in addition to their deep impact on the biological molecules. This enormous power of ionic solutions is based on the interactions of ion with solvent. In this work, we present some interesting results with comprehensive implications on the application of ion-solvent (i-s) interactions on organic reactions. Ion-Solvent interactions Cohesion among molecules in the liquid phase results from intermolecular forces. These forces include hydrogen-bonding, dipole-dipole, multi polar, dispersion interactions and also interactions emerging from the repulsion between two molecules. The cohesion due to intermolecular forces gives rise to a 'pressure' which is experienced by the solvent molecules. A liquid undergoing a small, isothermal volume expansion does work against the cohesive forces which causes a change in the internal energy, U. The function (∂U/∂V)T, is called as internal pressure (Pi) of a liquid and is supported by the equation of state. Internal pressure increases upon the addition of some solutes like NaCl, KCI, etc. and decreases by salts like of guanidinium salts. Diels-Alder Reaction in aqueous medium For long time water was not a popular solvent for the Diels-Alder reaction. Before 1980 its use had been reported only incidentally. Diels and Alder themselves performed the reaction between furan and maleic acid in an aqueous medium in 1931,27 an experiment which was repeated by Woodward and Baer in 1948. 28 They noticed a change in endo-exo selectivity when comparing the reaction in water with ether. The extreme influence of water can exert on the Diels-Alder reaction was rediscovered by Breslow in 1980, much by coincidence 29,30 while studying the effect of β-cyclodextrin on the rate of a Diels-Alder reaction in water, accidentally. Schem 1. Alternatively, Grieco et al., have repeatedly invoked the internal pressure of water as an explanation of the rate enhancement of Diels-Alder reactions in these solvents. 31 They probably inspired by the well known large effects of the external pressure on rates of cycloadditions. However the internal pressure of water is very low and offers no valid explanation for its effects on the Diels-Alder reaction. The internal pressure is defined as the energy required bringing about an infinitesimal change in the volume of the solvent at constant temperature. Due to the open and relatively flexible hydrogen-bond network of water, a small change in volume of these solvents does not require much energy. A related, but much more applicable solvent parameter is the cohesive energy density. This quantity is a measure of energy required for evaporation of the solvent per unit volume. The reactions in water were less accelerated by pressure than those in organic solvents, which is in line with notion that pressure diminishes hydrophobic interactions. The effect of water on the selectivity of Diels-Alder reactions Three years after the Breslow report on the large effects of water on the rate of the Diels-Alder reaction, he also demonstrated that the endo-exo selectivity of this reaction benefits markedly from employing aqueous media. Based on the influence of salting-in and salting-out agents, Breslow pinpoints hydrophobic effects as the most important contributor to the enhanced endo-exo selectivity. Hydrophobic effects are assured to stabilize the more compact endo transition state more than the extended exo transition state. In Breslow option the polarity of water significantly enhances the endo-exo selectivity. In conclusion, the special influence of water on the endo-exo selectivity seems to be a result of the fact that this solvent combines in it three characteristics that all favors formation of the endo/exo adduct. 1. water is strong hydrogen bond donor 2. water is polar and water induces hydrophobic interactions. Study of salting-out and salting-in reagents towards the Diels-Alder reaction of piperine (1): The special effects of water as solvent for valuable Diels-Alder reaction (Scheme 1) of piperine (1), greatly altered by the addition of ionic solutes (Table 1) such as LiCl, LiBr, LiClO4,- NaCl, NaBr, KF, KCl, KBr, MgCl2, CaCl2, guanidinium chloride, guanidinium carbonate, guanidinium nitrate. Aqueous salts solutions accelerated cycloaddition reactions (Scheme 1) of piperine (1) to give resultant cycloadducts 2, 3 and 4 among them 2 is major ortho-exo cyclohexene type dimeric amide alkaloid and also known as chabamide, which is previously isolated from this plant, isomer 3 is also known adduct and previously isolated from Piper nigrum. 21 Cycloadduct 4 was synthesized from piperine by Diels-Alder reaction by Wei. et al. its physical and spectroscopic data were identical with reported data22 (1H-NMR & Mass spectra). Table 1: Study of different salts towards the Diels-Alder reaction of piperine (1). aOverall yield of adducts after HPLC, un-reacted piperine was recovered in all reactions. Reaction showed good overall yield and more exo selectivity. This reaction showed completely regioselectivity (yield of 2+3>4) due to maximum involvement of α-double bond rather than γ-double bond of 1 during Diels-Alder reaction. Table 2: Comparision of salting-out and salting-in reagents towards the Diels-Alder reaction of piperine (1). Study of Salting-out reagents Increased rate in Diels-Alder reaction (over all yield up to 79 %) of piperine (1) has been attributed to the hydrophobic effect. Owing to the difference in polarity between water and the reactants, water molecules tend to associate amongst themselves, excluding the organic reagents and forcing them to associate together forming small drops surrounded by water. A further method of increasing the rate of Diels-Alder reaction in water is so called ‘salting-out’ effect. Among the salting-out reagents used (Table 1) in this methodology CaCl2 is the best reagent and gave 79 % over all yield. If anion size increases, reaction yield decreases, where as cation size increases, reaction yield increases. Here a salt such as calcium chloride is added to the aqueous solution. In this case water molecules attracted to the polar ions, increasing the internal pressure and reducing the volume. This has the effect of further excluding the organic reagents. For reactions such as Diels-Alder, which have negative activation volumes, the rates are enhanced by this increase in internal pressure in much the same way as expected for an increase in external pressure. This salting-out reagent showed good exo selectivity, due to formation of cycloadduct 2 (ortho-exo) is major up to 69 % (cycloadduct ratio) compare to cycloadducts 3 (21 %, meta-exo) and 4 (10%, meta-exo) are poor in yield. Schem 2. Plausible mechanism of Diels-Alder reaction catalyzed by Gn.HCl. Study of Salting-in reagents Among the tested salting-in reagents used in this methodology (Table 1) guanidinium chloride (Gn.HCL) is the best reagent and gave 81 % overall yield, where as LiClO4 end up with only 15 % overall yield. Gn.HCL reagent exhibited well selectivity towards the Diels-Alder reaction of piperine in given conditions (scheme 1). Formation of cycloadduct 2 in 80 %, 3 in 15 % and 4 in 5 % ratio is clearly indicates this methodology received good attention towards the exo selectivity in Diels-Alder reaction of piperine. Overall yield is also high with salting-in reagents when compare to salting-out reagents. Procedure for aqueous ionic salts catalyzed Diels–Alder reactions of piperine (1): To a stirred mixture of piperine (1) (50.0 mg, 0.175 mmol), 6M aqueous guanidinium. Hydrochloride (2 mL) in a round bottom flask fitted with condenser and refluxed for 70 h in an oil bath. After completion of the reaction, monitored by TLC (dipped in 5% solution of phosphomolybdic acid in methanol and heating), the reaction mixture was cooled to room temperature and diluted with water (3 mL). Then extracted with EtOAc (2x5 mL), the combined organic layers were dried over anhydrous Na2SO4 and concentrated in vacuo. The residue obtained was then purified by reversed-phase (RP) HPLC (column: Phenomenex Luna C18, 250 x 10 mm, 10µ), solvent system: 80% acetonitrile in water, flow rate: 1.5 mL/min, to give pure compounds of adducts (2) 0.065 g, (3) 0.012 g and (4) 0.004 g. Cycloaddition reaction between piperine (1a) and pellitorine (1b): Our aim of this cycloaddition reaction is to explain to study different cycloadducts and selectivity of diene among piperine and pellitorine (Scheme 4). This biomimetic synthesis will explain the probability of diene, which participated in Diels-Alder reaction between piperine (1a) and pellitorine (1b) both were isolated from same plant (P. chaba). Nigramide N, which is formed biosynthetically via cycloaddition reaction between piperine and pellitorine, this adduct previously isolated from roots of P. nigrum 21 by Wei. et. al. Lewis acid catalyzed cycloaddition reactions of piperine (1a) and pellitorine (1b) under organic and aqueous solvent conditions to give resultant cycloadducts 2c, 3c, 4c, 2a and 3b. Cycloadduct 2c and 3c is new cycloadducts and their structures were illustrated by 1D and 2D spectral data. Structure elucidation of compound 2c: Compound 2c was obtained as pale yellow liquid. The molecular formula of 2c was established as C31H44N2O4 by HRESIMS (Fig-18), which provided a molecular ion peak at m/z 509.3381 [M++H], in conjunction with its 13C NMR spectrum (Fig-12). The IR spectrum displayed absorption bands diagnostic of carbonyl (1640 cm-1) (Fig-10). The 300 MHz 1H NMR spectrum (in CDCl3) indicated the presence of two signals at δ 5.86 (dd, J = 15.6, 10.1 Hz) and 6.27 (d, J = 15.6 Hz), which were assigned to trans-olefinic protons by the coupling constant of 15.6 Hz. It also displayed aromatic protons due to two 1, 3, 4-trisubstituted aromatic rings at δ 6.82 (1H, br s), 6.76 (1H, dd, J = 7.8, 1.4 Hz), 6.75 (1H, d, J = 7.8 Hz) (Fig-11), (Table 4). In addition to the above-mentioned moieties, combined inspection of 1H NMR and 1H–1H COSY revealed the presence of cyclohexene ring, one isobutylamide and one pyrrolidine ring. The 13C NMR spectrum (Fig-12) displayed the presence of 31 carbon atoms and were further confirmed by DEPT experiments (Fig-13) into categories of 11 methylenes, 12 methines and 5 quaternary carbons including two carbonyls (δ 173.01 and 172.50). On the basis of these characteristic features, database and literature search led the skeleton of compound 2c as a dimeric alkaloidal framework. A comprehensive analysis of the 2D NMR data of compound 2c facilitated the proton and carbon assignments. 1H–1H COSY spectrum (Fig-16) suggested the sequential correlations of δ 3.51 (dq, J = 5.0, 2.6 Hz)/5.62 (dt, J = 9.8, 2.6 Hz)/6.10 (ddd, J = 9.8, 1.5 Hz)/2.20 (m)/2.72 (ddd, J = 11.1, 10.1, 5.2 Hz)/3.35 (dd, J = 11.1, 9.8 Hz) assignable to H-2-H-3-H-4-H-5-H-3"-H-2" of the cyclohexene ring. Concerning the connections of the n-amyl and 3, 4-methylenedioxy styryl groups, HMBC spectrum (Fig-15) showed correlations of H-4, H-6, H-7/C-5; H-5", H-4"/C-3", which implies that these units were bonded to the cyclohexene ring at C-5 and C-3". Further, HMBC correlations of two methylene protons at δ 5.95 with 147.91 (C-8"), 146.87 (C-9"), confirmed the location of methylenedioxy group at C-8", and C-9". Remaining units, isobutylamine and pyrrolidine (rings) were connected through carbonyl groups at C-2 and C-2", which was confirmed by HMBC correlations of H-2 and H-1' to C-1 (δ 173.01) and H-2" and H-1''' to C-1" (δ 172.50). The assignment of the relative configuration of compound 2c, and confirmation of overall structure were achieved by the interpretation of the NOESY spectral data and by analysis of 1H NMR coupling constants. The large vicinal coupling constants of H-2"/H-2 (11.1 Hz) and H-2"/H-3" (11.1 Hz) indicated anti-relations of H-2"/H-2 and H-2"/H-3" and the axial orientations for these protons. In the NOESY spectrum (Fig-17), the occurrence of the correlations between H-2/H-3" and the absence of NOE effects between H-2/H-2" and H-2"/H-3" supported the above result. This data indicated β-orientation for H-2" and α-orientation for H-2 and H-3". The α-orientation of H-5 was suggested by the coupling constant of H-5/H-3" (5.2 Hz) and the absence of the NOESY correlations between H-3" and H-2". On the basis of these spectral data, the structure of compound 2c was unambiguously established and trivially named as chabamide M. Compound 3a: IR (KBr) nmax: 2923, 2855,1628, 1489, 1242, 1128, 1035 cm-1 d ppm 0.69 & 1.25 (2H, m, H-2'"), 1.15 & 1.23 (2H, m, H-4'"), 1.31 & 1.40 (2H, m, H-3'"), 1.52 (2H, m, H-2'), 1.56 (2H, m, 4'), 1.61 (2H, m, H-3'), 2.94 (1H, td, J = 10.1, 10.1, 5.5 Hz, H-3"), 3.02 & 3.60 (2H, m, H-5'"), 3.09 & 3.32 (2H, m, H-1'"), 3.51 (2H, m, H-1'), 3.61 (1H, m, H-2), 3.61 (2H, m, H-5'), 3.78 (1H, dq, J = 10.0, 2.3 Hz, H-5), 4.07 (1H, t, J = 10.1, H-2"), 5.72 (1H, ddd, J = 9.8, 5.0, 2.7 Hz, H-3), 5.88 (2H, s, H-12), 5.89 (1H, dt, 10.3, 1.8 Hz, H-4), 5.90 (1H, J =15.8, 9.8 Hz, H-4"), 5.92 (1H, s, H-12"), 6.37 (1H, d, J = 15.8 Hz, H-5"), 6.68 (1H, brs, H-7), 6.69 (1H, d, J = 8.0 Hz, H-10"), 6.70 (1H, dd, J = 8.0, 1.4 Hz, H-11), 6.69 (1H, d, J = 8.0 Hz, H-10), 6.74 (1H, dd, J = 8.0, 1.6 Hz, H-11"), 6.79 (1H, brs, H-7"). ESIMS (m/z): 571 [M+ +H] Table 4: 1H & 13C NMR data of cycloadduct 2c in CDCl3 (300 MHz, δ in ppm, mult, J in Hz) Compound 4a: IR (KBr) nmax: 2926, 2857,1627, 1484, 1440, 1240, 1034 cm-1 1H NMR (300 MHz, CDCl3): d ppm 0.81 & 1.35 (2H, m, H-2'), 1.29 & 1.47 (2H, m, H-4'), 1.35 (2H, m, H-2"'), 1.36 & 1.51 (1H, m, H-3'), 1.47 (2H, m, H-4"'), 1.51 (2H, m, H-3"'), 2.92 (2H, m, H-1"'), 2.99 (1H, ddd, J = 12.5, 9.7, 5.5 Hz, H-4"), 3.22 (2H, m, H-1'), 3.29 & 3.71 (2H, m, H-5'), 3.38 (1H, m, H-4"'), 3.44 (1H, dd, J = 12.1, 10.1 Hz, H-5"), 3.59 (1H, t, J = 5.3 Hz, H-5), 3.70 (1H, dq, J = 12.1, 2.1, H-2), 5.65 (1H, dd, J = 15.6, 9.5 Hz, H-3"), 5.70 (1H, dt, J = 9.9, 1.6, H-3), 5.81 (1H, d, J = 15.6 Hz, H-2"), 5.84 (1H, s, H-12"), 5.90-5.92 (2H, brs, H-12), 5.96 (1H, ddd, J = 9.2, 5.8, 2.6 Hz, H-4), 6.55 (1H, dd, J =7.9, 1.5 Hz, H-11"), 6.61 (1H, d, J = 8.2 Hz, H-10"), 6.62 (1H, d, J = 1.4 Hz, H-7"), 6.79 (1H, d, J = 7.9 Hz, H-10), 6.92 (1H, dd, J = 8.0, 1.5 Hz, H-11), 7.01 (1H, d, J = 1.5 Hz, H-7). ESIMS (m/z): 571 [M+ +H] Acknowledgements The authors are thankful to Director IICT for his constant encouragement and CSIR New Delhi for providing the fellowship References Braun, M. Synth. Highlights 1991, 232 Robinson, R. Chem. Soc. 1917, 762. Stork, G.; Burgstahler, A. W. Am. Chem. Soc. 1955, 38, 1890. Johnson, W. S.; Gravestock, M. B.; McCarry, B. E. Am. Chem. Soc. 1971, 93, 4332. Chapman, O. L.; Engel, M. R.; Springer, J. P.; Clardy, J. C. Am. Chem. Soc. 1971, 93, 6696. Bandaranayake, W. M.; Banfield, J. E.; Black, D. St. C. Chem. Soc., Chem Commun. 1980, 902. Nicolaou, K. C.; Zipkin, R. E.; Petasis, N. A. Am. Chem. Soc. 1982, 104, 5558. O.; Alder, K. Ann. 1928, 460, 98. Woodward, R. B.; Hoffmann, R. Chem. 1969, 81, 797. Fakui, K. Chem. Res. 1971, 4, 57. Houk, K. N. Chem.. Res. 1975, 8, 361. Houk, K. N.; Li, Y.; Evanseck, D. Angew Chem., Ed. Engl. 1992, 31, 682. Alder, K.; Stein, G. Chem. 1937, 50, 510. Fotiadu, F.; Michel, F.; Buono, G. Tetraheron Lett. 1990, 34, 4863. Gleiter, R.; Bohm, M. C. Pure Appl. Chem. 1983, 55, 237. Woodward, R. B.; Katz, T. J. Terahedron 1958, 5, 70. Kakushima, M. J. Chem. 1979, 57, 2564. Houk, K. N. Tetrahedron Lett. 1970, 30, 2621. Houk, K. N.; Luskus, L. J. Am. Chem. Soc. 1971, 93, 4606. Otto, S.; Bertoncin, F.; Engberts, J.B. F. N. Am. Chem. Soc., 1996, 118, 7702–7707. Wei, K.; Li, W.; Koike, K.; Chen, Y-J.; Nikaido, T. Org. Chem. 2005, 70, 1164. Wei, K.; Li, W.; Koike, K.; Chen, Y-J.; Nikaido, T. Lett. 2005, 7, 2833–2835. Rukachaisirikul, T.; Prabpai, S.; Champung, P.; Suksamrarn, A. Planta Med. 2002, 68, 850-853. Nagao, Y.; Seno, K.; Kawabata, K.; Miyasaka, T.; Takao, S.; Fujita, Tetrahedron Lett. 1980, 21, 841. Otto, S.; Boccaletti, G.; Engberts, J. B. F. N. Am. Chem. Soc. 1998, 120, 4238–4239. Otto, S.; Bertoncin, F.; Engberts, J. B. F. N. Am. Chem. Soc. 1996, 118, 7702–7707. O.; Alder, K. Ann. 1931, 490, 243. Woodward, R. B.; Baer, H. Am. Chem. Soc. 1948, 70, 1161. Breslow, R.; Rideout, D. C. Am. Chem. Soc. 1980, 102, 7816. Breslow, R.; Guo, T. Am. Chem. Soc. 1988, 110, 5613. Grieco, P.A.; Nunes, J. J.; Gaul, M. D. Am. Chem. Soc. 1990, 112, 4595.

Abstract In this paper, we discuss the vacuum structure of the gauge-Higgs unification theory, which is one of the attractive candidates of physics beyond the standard model. This scenario has a remarkable feature, namely it has infinitely degenerate vacua due to the characteristic periodic potential of the Higgs filed, to be identified with the extra space component of the higher dimensional gauge field. We address a question, whether to form the superposition of such degenerate vacua, like the θ-vacuum in QCD, is necessary or not, in order to realize the true vacuum state of the theory. We derive gauge field configuration which describes the transition between neighboring vacua, like the instanton (or anti-instanton) solution in QCD, and the corresponding Euclidean action in two models. In a simplified 2-dimensional U(1) model, the derived configuration to describe the transition is shown to have finite Euclidean action, and accordingly the “θ-vacuum” and the resultant “θ-term” are formulated. In a realistic 5D U(1) model, however, the gauge field configuration to describe the transition is shown to have infinite Euclidean action and therefore the tunneling probability between the degenerate vacua vanishes. Thus the superposition of the degenerate vacua is not necessary.

Abstract Gaugino condensation on D-branes wrapping internal cycles gives a mechanism to stabilize the associated moduli. According to the effective field theory, this gives rise, when combined with fluxes, to supersymmetric AdS4 solutions. In this paper we provide a ten-dimensional description of these vacua. We first find the supersymmetry equations for type II AdS4 vacua with gaugino condensates on D-branes, in the framework of generalized complex geometry. We then solve them for type IIB compactifications with gaugino condensates on smeared D7-branes. We show that supersymmetry requires a (conformal) Calabi-Yau manifold and imaginary self-dual three-form fluxes with an additional (0,3) component. The latter is proportional to the cosmological constant, whose magnitude is determined by the expectation value of the gaugino condensate and the stabilized volume of the cycle wrapped by the branes. This confirms, qualitatively and quantitatively, the results obtained using effective field theory. We find that exponential separation between the AdS and the KK scales seems possible as long as the three-form fluxes are such that their (0,3) component is exponentially suppressed. As for the localized solution, it requires going beyond SU(3)-structure internal manifolds. Nevertheless, we show that the action can be evaluated on-shell without relying on the details of such complicated configuration. We find that no “perfect square” structure occurs, and the result is divergent. We compute the four-fermion contributions, including a counterterm, needed to cancel these divergences.

Abstract We derive a closed-form false vacuum decay rate at one loop in the thin wall limit, where the true and false vacua are nearly degenerate. We obtain the bounce configuration in D dimensions, together with the Euclidean action with a higher order correction, counter-terms and renormalization group running. We extract the functional determinant via the Gel’fand-Yaglom theorem for low and generic orbital multipoles. The negative and zero eigenvalues appear for low multipoles and the translational zeroes are removed. We compute the fluctuations for generic multipoles, multiply and regulate the orbital modes. We find an explicit finite renormalized decay rate in D = 3, 4 and give a closed-form expression for the finite functional determinant in any dimension.

Abstract Non-supersymmetric string models are plagued with tadpoles for dynamical fields, which signal uncanceled forces sourced by the vacuum. We argue that in certain cases, uncanceled dynamical tadpoles can lead to inconsistencies with quantum gravity, via violation of swampland constraints. We describe an explicit realization in a supersymmetric toroidal Z2 × Z2 orientifold with D7-branes, where the dynamical tadpole generated by displacement of the D7-branes off its minimum leads to violation of the axion Weak Gravity Conjecture. In these examples, cancellation of dynamical tadpoles provides consistency conditions for the configuration, of dynamical nature (as opposed to the topological conditions of topological tadpoles, such as RR tadpole cancellation in compact spaces). We show that this approach provides a re-derivation of the Z-minimization criterion for AdS vacua giving the gravitational dual of a-maximization in 4d $$ \mathcal{N} $$ N = 1 toric quiver SCFTs.

Abstract We consider spacetime-dependent solutions to string theory models with tadpoles for dynamical fields, arising from non-trivial scalar potentials. The solutions have necessarily finite extent in spacetime, and are capped off by boundaries at a finite distance, in a dynamical realization of the Cobordism Conjecture. We show that as the configuration approaches these cobordism walls of nothing, the scalar fields run off to infinite distance in moduli space, allowing to explore the implications of the Swampland Distance Conjecture. We uncover new interesting scaling relations linking the moduli space distance and the SDC tower scale to spacetime geometric quantities, such as the distance to the wall and the scalar curvature. We show that walls at which scalars remain at finite distance in moduli space correspond to domain walls separating different (but cobordant) theories/vacua; this still applies even if the scalars reach finite distance singularities in moduli space, such as conifold points.We illustrate our ideas with explicit examples in massive IIA theory, M-theory on CY threefolds, and 10d non-supersymmetric strings. In 4d $$ \mathcal{N} $$ N = 1 theories, our framework reproduces a recent proposal to explore the SDC using 4d string-like solutions.

The [Formula: see text] heterotic string orbifold yielded a large space of phenomenological three generation models and serves as a testing ground to explore how the Standard Model of particle physics may be incorporated in a theory of quantum gravity. In this paper, we explore the existence of type 0 models in this class of string compactifications. We demonstrate the existence of type 0 [Formula: see text] heterotic string orbifolds, and show that there exist a large degree of redundancy in the space of GGSO projection coefficients when the type 0 restrictions are implemented. We explore the existence of such configurations in several constructions. The first correspond to essentially a unique configuration out of a priori [Formula: see text] discrete GGSO choices. We demonstrate this uniqueness analytically, as well as by the corresponding analysis of the partition function. A wider classification is performed in [Formula: see text]-models and [Formula: see text]-models, where the first class correspond to compactifications of a tachyonic ten-dimensional heterotic string vacuum, whereas the second correspond to compactifications of the ten-dimensional nontachyonic [Formula: see text]. We show that the type 0 models in both cases contain physical tachyons at the free fermionic point in the moduli space. These vacua are therefore necessarily unstable, but may be instrumental in exploring the string dynamics in cosmological scenarios. We analyze the properties of the string one-loop amplitude. Naturally, these are divergent due to the existence of tachyonic states. We show that once the tachyonic states are removed by hand the amplitudes are finite and exhibit a form of misaligned supersymmetry.