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Journal articles on the topic 'Supersymmetric field theorie'

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Published: 9 March 2023

Last updated: 10 March 2023

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1

HOWE, P. S., and K. S. STELLE. "THE ULTRAVIOLET PROPERTIES OF SUPERSYMMETRIC FIELD THEORIES." International Journal of Modern Physics A 04, no. 08 (May 10, 1989): 1871–912. http://dx.doi.org/10.1142/s0217751x89000753.

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We review the structure of ultraviolet divergence cancellations in supersymmetric field theories. We discuss the various nonrenormalization theorems of superspace perturbation theory, both for extended and for simple supersymmetry. These theorems and the background field method are applied to super Yang-Mills theories in four and higher dimensions, to supergravity theories and to two-dimensional supersymmetric nonlinear σ-models.

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2

ÜLKER, K. "ON THE COHOMOLOGICAL STRUCTURE OF SUPERSYMMETRIC LAGRANGIANS WITH AND WITHOUT AUXILIARY FIELDS." Modern Physics Letters A 16, no. 13 (April 30, 2001): 881–89. http://dx.doi.org/10.1142/s0217732301003991.

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The origin of non-renormalization theorems in field theories with global supersymmetry can be traced to the fact that supersymmetric actions can be viewed as the highest components of respective supermultiplets. Supersymmetric interactions in particular can therefore be represented as supersymmetry variations of lower-dimensional field polynomials. We investigate here this algebraic structure in the context of the Wess–Zumino model and N = 1 and N = 2 supersymmetric Yang–Mills theories.

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3

LLEDÓ, M. A. "DEFORMED SUPERSYMMETRIC FIELD THEORIES." Modern Physics Letters A 16, no. 04n06 (February 28, 2001): 305–10. http://dx.doi.org/10.1142/s0217732301003395.

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We make a short review on the Moyal–Weyl star products with emphasis in its convergence. We consider field theories on a deformed superspace and analyze the compatibility of such products with supersymmetry. We investigate some aspects of the Wess–Zumino model, super-Yang–Mills theories and analyze the correspondence of the latter with the supersymmetric Born–Infeld action.

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4

DI STEFANO, ROSANNE, MAXIMILIAN KREUZER, and ANTON REBHAN. "ON THE CANONICAL FORMULATION OF SUPERSYMMETRIC YANG-MILLS THEORIES." Modern Physics Letters A 02, no. 07 (July 1987): 487–97. http://dx.doi.org/10.1142/s0217732387000604.

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We treat supersymmetric Yang-Mills theories in the canonical formulation. By a gauge invariant and Lorentz covariant ansatz for the canonical supersymmetry generators we rederive that supersymmetric theories based on spin 1 and spin [Formula: see text] exist only in dimensions 4, 6, and 10. Moreover we find that the algebra of these supersymmetry generators closes on the phase space without the need of auxiliary fields. This holds true also for the higher-dimensional theories where it is not possible to find auxiliary fields making the algebra close off-shell on the Lagrangian level.

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5

CLARK, T. E., and S. T. LOVE. "THE SUPERCURRENT IN SUPERSYMMETRIC FIELD THEORIES." International Journal of Modern Physics A 11, no. 16 (June 30, 1996): 2807–21. http://dx.doi.org/10.1142/s0217751x9600136x.

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A supercurrent superfield whose components include a conserved energy-momentum tensor and supersymmetry current as well as an (generally broken) R symmetry current is constructed for a generic effective N=1 supersymmetric gauge theory. The general form of the R symmetry breaking is isolated. Included within the various special cases considered is the identification of those models which exhibit an unbroken R symmetry. One such example corresponds to a nonlinearly realized gauge symmetry where the chiral field R weight is required to vanish.

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6

NISHINO, HITOSHI, and SUBHASH RAJPOOT. "HODGE DUALITY AND COSMOLOGICAL CONSTANT." Modern Physics Letters A 21, no. 02 (January 20, 2006): 127–41. http://dx.doi.org/10.1142/s0217732306019372.

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We present a simple mechanism to eliminate cosmological constants both in supersymmetric and non-supersymmetric theories. This mechanism is based on the Hodge (Poincaré) duality between a 0-form and D-form field strengths in D-dimensional spacetime. The new key ingredient is the introduction of an extra Chern–Simons term into the D-form field strength H dual to the 0-form field strength. Our formulation can also be made consistent with supersymmetry. Typical applications to four-dimensional N = 1 supergravity and to ten-dimensional type IIA supergravity are given. The success of our formulation for both supersymmetric and non-supersymmetric systems strongly indicates the validity of our mechanism even after supersymmetry breakings at the classical level. Our mechanism may well be applicable to quantized systems, at least for supersymmetric cases with fundamental D-brane actions available.

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7

TKACH, V. I., J. J. ROSALES, and J. SOCORRO. "SPONTANEOUS BREAKING OF SUPERSYMMETRY IN COSMOLOGICAL MODELS AND SUPERGRAVITY THEORIES." Modern Physics Letters A 14, no. 18 (June 14, 1999): 1209–16. http://dx.doi.org/10.1142/s0217732399001309.

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In this work we have constructed the most general action for a set of complex homogeneous scalar supermultiplets interacting with the scale factor in the supersymmetric FRW model. It is shown that the local conformal time supersymmetry leads to a scalar field potential defined in terms of the Kähler potential and superpotential in the same combination as in supergravity (or effective superstring) theories. This scalar field potential depends on an arbitrary parameter α which is not fixed by conformal time supersymmetry and induces the spontaneous breaking of supersymmetry in supergravity theories.

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8

Faux, M. G., K. M. Iga, and G. D. Landweber. "Dimensional Enhancement via Supersymmetry." Advances in Mathematical Physics 2011 (2011): 1–45. http://dx.doi.org/10.1155/2011/259089.

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We explain how the representation theory associated with supersymmetry in diverse dimensions is encoded within the representation theory of supersymmetry in one time-like dimension. This is enabled by algebraic criteria, derived, exhibited, and utilized in this paper, which indicate which subset of one-dimensional supersymmetric models describes “shadows” of higher-dimensional models. This formalism delineates that minority of one-dimensional supersymmetric models which can “enhance” to accommodate extra dimensions. As a consistency test, we use our formalism to reproduce well-known conclusions about supersymmetric field theories using one-dimensional reasoning exclusively. And we introduce the notion of “phantoms” which usefully accommodate higher-dimensional gauge invariance in the context of shadow multiplets in supersymmetric quantum mechanics.

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9

Mihaila, L. "Precision Calculations in Supersymmetric Theories." Advances in High Energy Physics 2013 (2013): 1–64. http://dx.doi.org/10.1155/2013/607807.

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In this paper we report on the newest developments in precision calculations in supersymmetric theories. An important issue related to this topic is the construction of a regularization scheme preserving simultaneously gauge invariance and supersymmetry. In this context, we discuss in detail dimensional reduction in component field formalism as it is currently the preferred framework employed in the literature. Furthermore, we set special emphasis on the application of multi-loop calculations to the analysis of gauge coupling unification, the prediction of the lightest Higgs boson mass, and the computation of the hadronic Higgs production and decay rates in supersymmetric models. Such precise theoretical calculations up to the fourth order in perturbation theory are required in order to cope with the expected experimental accuracy on the one hand and to enable us to distinguish between the predictions of the Standard Model and those of supersymmetric theories on the other hand.

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10

NEPOMECHIE, RAFAEL I. "SUPERSYMMETRY IN THE BOUNDARY TRICRITICAL ISING FIELD THEORY." International Journal of Modern Physics A 17, no. 26 (October 20, 2002): 3809–26. http://dx.doi.org/10.1142/s0217751x02012119.

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We argue that it is possible to maintain both supersymmetry and integrability in the boundary tricritical Ising field theory. Indeed, we find two sets of boundary conditions and corresponding boundary perturbations which are both supersymmetric and integrable. The first set corresponds to a "direct sum" of two nonsupersymmetric theories studied earlier by Chim. The second set corresponds to a one-parameter deformation of another theory studied by Chim. For both cases, the conserved supersymmetry charges are linear combinations of Q, [Formula: see text] and the spin-reversal operator Γ.

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11

Jarlskog, Cecilia. "Supersymmetry: Early Roots That Did Not Grow." Advances in High Energy Physics 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/764875.

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This paper is about early roots of supersymmetry, as found in the literature from 1940s and early 1950s. There were models where the power of “partners” in alleviating divergences in quantum field theory was recognized. However, other currently known remarkable features of supersymmetry, such as its role in the extension of the Poincaré group, were not known. There were, of course, no supersymmetric nonabelian quantum field theories in those days.

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12

KUROKI, TSUNEHIDE, and FUMIHIKO SUGINO. "SPONTANEOUS SUPERSYMMETRY BREAKING BY LARGE-N MATRICES." International Journal of Modern Physics A 23, no. 14n15 (June 20, 2008): 2192–94. http://dx.doi.org/10.1142/s0217751x08040809.

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Motivated by supersymmetry breaking in matrix model formulations of superstrings, we present some concrete models, in which the supersymmetry is preserved for any finite N, but gets broken at infinite N, where N is the rank of matrix variables. The models are defined as supersymmetric field theories coupled to some matrix models, and in the induced action obtained after integrating out the matrices, supersymmetry is spontaneously broken only when N is infinity.

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13

HABARA, YOSHINOBU, YUKINORI NAGATANI, HOLGER B. NIELSEN, and MASAO NINOMIYA. "DIRAC SEA AND HOLE THEORY FOR BOSONS I: A NEW FORMULATION OF QUANTUM FIELD THEORIES." International Journal of Modern Physics A 23, no. 18 (July 20, 2008): 2733–69. http://dx.doi.org/10.1142/s0217751x08040342.

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Bosonic formulation of the negative energy sea, so-called Dirac sea, is proposed by constructing a hole theory for bosons as a new formulation of the second quantization of bosonic fields. The original idea of Dirac sea for fermions, where the vacuum state is considered as a state completely filled by fermions of negative energy and holes in the sea are identified as antiparticles, is extended to boson case in a consistent manner. The bosonic vacuum consists of a sea filled by negative energy bosonic states, while physical probabilities become always positive definite. We introduce a method of the double harmonic oscillator to formulate the hole theory of bosons. Our formulation is also applicable to supersymmetric field theory. The sea for supersymmetric theories has an explicit supersymmetry. We suggest applications of our formulations to the anomaly theories and the string theories.

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14

Gallego, Diego. "Light field integration in SUGRA theories." International Journal of Modern Physics A 30, no. 01 (January 9, 2015): 1550003. http://dx.doi.org/10.1142/s0217751x15500037.

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We revisit the integration of fields in 𝒩 = 1 Supergravity with the requirement that the effective theory has a reliable two-derivative supersymmetric description. In particular, we study, in a supersymmetric manifest way, the situation where the fields that are mapped out have masses comparable to the Supersymmetry breaking scale and masses of the remaining fields. We find that as long as one stands in regions of the field configuration space where the analytic continuation to superspace of the F-flatness conditions be reliable equations of motion for the fields that are being mapped out, and provided their solutions are stable regardless the dynamics of the remaining fields, such a two-derivative description is a reliable truncation of the full effective theory. The study is mainly focused to models with two chiral sectors, H and L, described by a Kähler invariant function with schematic dependencies of the form [Formula: see text], which leads to a nearly decoupled theory that allows the previous requirements to be easily satisfied in a consistent way. Interestingly, enough for the matters of our study, this kind of models present a scenario that is as safe as the one presented in sequestered models. It is also possible to allow gauge symmetries as long as these appear also factorized in hidden and visible sectors. Then, the integration of the hidden vector superfields is compulsory and proceeds reliably through the D-flatness condition analytically continued to superspace.

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15

GATTO, R., and G. SARTORI. "RELICS OF SUPERSYMMETRY IN THE MASS SPECTRUM AFTER SPONTANEOUS BREAKING." International Journal of Modern Physics A 01, no. 03 (October 1986): 683–92. http://dx.doi.org/10.1142/s0217751x86000253.

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We determine, at the classical level, the constraints on the mass spectrum imposed by the complex symmetries underlying quantum field theories with globally supersymmetric Lagrangians, in case of spontaneous breaking of the internal symmetry and/or supersymmetry, both in case of global and local internal symmetry.

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16

KUZNETSOVA, Z., M. ROJAS, and F. TOPPAN. "ON SUPERGROUPS WITH ODD CLIFFORD PARAMETERS AND SUPERSYMMETRY WITH MODIFIED LEIBNIZ RULE." International Journal of Modern Physics A 23, no. 02 (January 20, 2008): 309–26. http://dx.doi.org/10.1142/s0217751x08038159.

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We investigate supergroups with Grassmann parameters replaced by odd Clifford parameters. The connection with nonanticommutative supersymmetry is discussed. A Berezin-like calculus for odd Clifford variables is introduced. Fermionic covariant derivatives for supergroups with odd Clifford variables are derived. Applications to supersymmetric quantum mechanics are made. Deformations of the original supersymmetric theories are encountered when the fermionic covariant derivatives do not obey the graded Leibniz property. The simplest nontrivial example is given by the N = 2 supersymmetric quantum mechanics with a real (1, 2, 1) multiplet and a cubic potential. The action is real. Depending on the overall sign ("Euclidean" or "Lorentzian") of the deformation, a Bender–Boettcher pseudo-Hermitian Hamiltonian is encountered when solving the equations of motions of the auxiliary field. A possible connection of our framework with the Drinfeld twist deformation of supersymmetry is pointed out.

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17

Pospelov, M. "Lorentz violation and super-symmetry." Canadian Journal of Physics 84, no. 6-7 (January 15, 2006): 669–75. http://dx.doi.org/10.1139/p06-043.

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We review recent progress in constructing supersymmetric field theories modified by the presence of constant vector and tensor backgrounds, or in other words SUSY field theories with Lorentz violation (LV). We show that the requirement of supersymmetry and gauge invariance limits the LV in the minimal supersymmetric Standard Model to dimension five and higher levels, giving a natural explanation to the smallness of the Lorentz violation. We show main phenomenological features of such models, among which is the absence of large LV corrections to dispersion relations, and include radiative corrections. We show that 1/MPlanck normalized corrections are ruled out at the 10–10 level. PACS Nos.: 11.30.Cp, 11.30.Pb, 11.10.Hi

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18

MAGGIORE, NICOLA. "OFF-SHELL FORMULATION OF N=2 SUPER YANG-MILLS THEORIES COUPLED TO MATTER WITHOUT AUXILIARY FIELDS." International Journal of Modern Physics A 10, no. 27 (October 30, 1995): 3937–50. http://dx.doi.org/10.1142/s0217751x95001844.

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N=2 supersymmetric Yang-Mills theories coupled to matter are considered in the Wess-Zumino gauge. The supersymmetries are realized nonlinearly and the anticommutator between two susy charges gives, in addition to translations, gauge transformations and equations of motion. The difficulties hidden in such an algebraic structure are well known: almost always auxiliary fields can be introduced in order to put the formalism off-shell, but still the field-dependent gauge transformations give rise to an infinite-dimensional algebra quite hard to deal with. However, it is possible to avoid all these problems by collecting into a unique nilpotent operator all the symmetries defining the theory, namely ordinary BRS, supersymmetries and translations. According to this method the role of the auxiliary fields is covered by the external sources coupled, as usual, to the nonlinear variations of the quantum fields. The analysis is then formally reduced to that of ordinary Yang-Mills theory.

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19

Esipova, S. R., P. M. Lavrov, and O. V. Radchenko. "Supersymmetric invariant theories." International Journal of Modern Physics A 29, no. 11n12 (April 25, 2014): 1450065. http://dx.doi.org/10.1142/s0217751x14500651.

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We study field models for which a quantum action (i.e. the action appearing in the generating functional of Green functions) is invariant under supersymmetric transformations. We derive the Ward identity which is a direct consequence of this invariance. We consider a change of variables in functional integral connected with supersymmetric transformations when its parameter is replaced by a nilpotent functional of fields. Exact form of the corresponding Jacobian is found. We find restrictions on generators of supersymmetric transformations when a consistent quantum description of given field theories exists.

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20

Ali, Sajid, Georg Bergner, Henning Gerber, Pietro Giudice, István Montvay, Gernot Münster, Stefano Piemonte, and Philipp Scior. "Ward identities in N = 1 supersymmetric SU(3) Yang-Mills theory on the lattice." EPJ Web of Conferences 175 (2018): 08003. http://dx.doi.org/10.1051/epjconf/201817508003.

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The introduction of a space-time lattice as a regulator of field theories breaks symmetries associated with continuous space-time, i.e. Poincaré invariance and supersymmetry. A non-zero gluino mass in the supersymmetric Yang-Mills theory causes an additional soft breaking of supersymmetry. We employ the lattice form of SUSY Ward identities, imposing that their continuum form would be recovered when removing the lattice regulator, to obtain the critical hopping parameter where broken symmetries can be recovered.

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21

Andrianopoli, Laura, and Lucrezia Ravera. "On the Geometric Approach to the Boundary Problem in Supergravity." Universe 7, no. 12 (November 28, 2021): 463. http://dx.doi.org/10.3390/universe7120463.

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We review the geometric superspace approach to the boundary problem in supergravity, retracing the geometric construction of four-dimensional supergravity Lagrangians in the presence of a non-trivial boundary of spacetime. We first focus on pure N=1 and N=2 theories with negative cosmological constant. Here, the supersymmetry invariance of the action requires the addition of topological (boundary) contributions which generalize at the supersymmetric level the Euler-Gauss-Bonnet term. Moreover, one finds that the boundary values of the super field-strengths are dynamically fixed to constant values, corresponding to the vanishing of the OSp(N|4)-covariant supercurvatures at the boundary. We then consider the case of vanishing cosmological constant where, in the presence of a non-trivial boundary, the inclusion of boundary terms involving additional fields, which behave as auxiliary fields for the bulk theory, allows to restore supersymmetry. In all the cases listed above, the full, supersymmetric Lagrangian can be recast in a MacDowell-Mansouri(-like) form. We then report on the application of the results to specific problems regarding cases where the boundary is located asymptotically, relevant for a holographic analysis.

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22

MOROZOV, A. YU, ANTTI J. NIEMI, and K. PALO. "GEOMETRIC APPROACH TO SUPERSYMMETRY." International Journal of Modern Physics B 06, no. 11n12 (June 1992): 2149–57. http://dx.doi.org/10.1142/s0217979292001079.

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We argue that a generic supersymmetric theory can be characterized entirely in terms of loop space symplectic geometry, either in a loop space parametrized by the bosonic variables or in a superloop space parametrized by half of the bosonic and fermionic variables. A Poincare supersymmetric theory is a realization of our construction in terms of space-time variables that admit a natural Lorentz-invariant interpretation. Our approach opens a new, geometric point of view to a large number of problems, including the mechanism of supersymmetry breaking and the structure of topological quantum field theories.

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23

JOSEPH, ANOSH. "SUPERSYMMETRIC YANG–MILLS THEORIES WITH EXACT SUPERSYMMETRY ON THE LATTICE." International Journal of Modern Physics A 26, no. 30n31 (December 20, 2011): 5057–132. http://dx.doi.org/10.1142/s0217751x11054863.

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Inspired by the ideas from topological field theory it is possible to rewrite the supersymmetric charges of certain classes of extended supersymmetric Yang–Mills (SYM) theories in such a way that they are compatible with the discretization on a Euclidean space–time lattice. Such theories are known as maximally twisted SYM theories. In this review we discuss the construction and some applications of such classes of theories. The one-loop perturbative renormalization of the four-dimensional lattice [Formula: see text] SYM is discussed in particular. The lattice theories constructed using twisted approach play an important role in investigating the thermal phases of strongly coupled SYM theories and also the thermodynamic properties of their dual gravitational theories.

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24

Choudhury, Sayantan, Sachin Panneer Selvam, and K. Shirish. "Circuit Complexity from Supersymmetric Quantum Field Theory with Morse Function." Symmetry 14, no. 8 (August 11, 2022): 1656. http://dx.doi.org/10.3390/sym14081656.

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Computation of circuit complexity has gained much attention in the theoretical physics community in recent times, to gain insights into the chaotic features and random fluctuations of fields in the quantum regime. Recent studies of circuit complexity take inspiration from Nielsen’s geometric approach, which is based on the idea of optimal quantum control in which a cost function is introduced for the various possible path to determine the optimum circuit. In this paper, we study the relationship between the circuit complexity and Morse theory within the framework of algebraic topology, which will then help us study circuit complexity in supersymmetric quantum field theory describing both simple and inverted harmonic oscillators up to higher orders of quantum corrections. We will restrict ourselves to N=1 supersymmetry with one fermionic generator Qα. The expression of circuit complexity in quantum regime would then be given by the Hessian of the Morse function in supersymmetric quantum field theory. We also provide technical proof of the well known universal connecting relation between quantum chaos and circuit complexity of the supersymmetric quantum field theories, using the general description of Morse theory.

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25

ARNONE, S., S. CHIANTESE, and K. YOSHIDA. "APPLICATIONS OF EXACT RENORMALIZATION GROUP TECHNIQUES TO THE NON-PERTURBATIVE STUDY OF SUPERSYMMETRIC GAUGE FIELD THEORY." International Journal of Modern Physics A 16, no. 11 (April 30, 2001): 1811–24. http://dx.doi.org/10.1142/s0217751x01004499.

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Exact Renormalization Group techniques are applied to supersymmetric models in order to get some insights into the low energy effective actions of such theories. Starting from the ultra-violet finite mass deformed N=4 supersymmetric Yang Mills theory, one varies the regularising mass and compensates for it by introducing an effective Wilsonian action. (Polchinski's) renormalization group equation is modified in an essential way by the presence of rescaling (a.k.a. Konishi) anomaly, which is responsible for the beta-function. When supersymmetry is broken up to N=1 the form of effective actions in terms of massless fields is quite reasonable, while in the case of the N=2 model we appear to have problems related to instantons.

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CASTRO, CARLOS. "THE SPINNING MEMBRANE, SUPER-SU(∞)-GAUGE THEORIES AND MOYAL BRACKETS." International Journal of Modern Physics A 07, no. 03 (January 30, 1992): 535–61. http://dx.doi.org/10.1142/s0217751x92000247.

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Several important topics concerning the membrane and its symmetries are discussed. The fact that a space–time-independent Lagrangian density for a gauge-field configuration of a (d – 1)-dimensional SU (∞) super Yang–Mills theory, reduced to one dimension (time), is equivalent to a Green–Schwarz formalism of the Euclidean Eguchi–Schild string action in d – 1 dimensions, naturally raises the question whether one can construct a Neveu–Ramond–Schwarz analog. The answer is in the negative; the world-sheet supersymmetric extension of the Eguchi–Schild action for the string cannot be viewed as a classical-vacuum configuration of a super-SU (∞)- gauge theory. For the second topic we construct a "supersymmetry" charge operator, Qf, which plays the role of a residual fermionic symmetry, for fixed time, of the light-cone spinning membrane. It is explicitly shown how the Yang–Mills type of actions and, in particular, the ones for vacuum-field configurations, associated with Q(∞) supergauge theories, are invariant under both Qf "supersymmetry" and the superalgebra of area-preserving superdiffeomorphisms of the light-cone spinning torus membrane, Q(∞). More general actions can be constructed which are invariant under deformations of this superalgebra. In this case the ordinary (graded) Poisson brackets are replaced by super Moyal brackets. Finally, we conjecture why these actions, in analogy with what happens with the light-cone supermembrane, should correspond to a superfiber bundle (over space–time) formulation of the supersymmetric-gauge quantum-mechanical models (SGQMM's) of Flume and Baake et al.; with the general supergroup of trigonometric structure constants of Fairlie, Fletcher and Zachos as the structure supergroup of the superfiber. To support our concluding conjecture, preliminary steps are outlined which are necessary in order to fix the light-cone gauge for the spinning-membrane action. We discuss why the Qf "supersymmetry" (the remnant world-volume light-cone local supersymmetry) and the Q(∞) supergauge transformations must arise as its residual symmetries.

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GRANDITS, PETER. "ON NON-SUPERSYMMETRIC FINITE QUANTUM FIELD THEORIES." International Journal of Modern Physics A 10, no. 10 (April 20, 1995): 1507–28. http://dx.doi.org/10.1142/s0217751x95000723.

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In a previous paper, requiring finiteness of Yukawa couplings in one-loop approximation, a no-go theorem for the finiteness of non-supersymmetric gauge theories with gauge group SU (n) was proven. Interestingly enough the gauge group SU(5), prominent in GUT models, was not covered by this proof. However, with somewhat more effort the no-go theorem can be extended to this case. Considering an even larger class of particle contents, we show that the number of possibly finite theories is greatly reduced. It should be stressed that our results are based upon two-loop finiteness of the gauge coupling, although in order to find really finite theories the finiteness conditions on the quartic scalar couplings have to be considered too.

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MAGGIORE, NICOLA. "ALGEBRAIC RENORMALIZATION OF N=2 SUPER YANG-MILLS THEORIES COUPLED TO MATTER." International Journal of Modern Physics A 10, no. 26 (October 20, 1995): 3781–801. http://dx.doi.org/10.1142/s0217751x95001789.

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We study the algebraic renormalization of N=2 supersymmetric Yang-Mills theories coupled to matter. A regularization procedure preserving both the BRS invariance and the supersymmetry is not known yet, so it is necessary to adopt the algebraic method of renormalization, which does not rely on any regularization scheme. The whole analysis is reduced to the solution of cohomology problems arising from the generalized Slavnov operator which summarizes all the symmetries of the model. Besides unphysical renormalizations of the quantum fields, we find that the only coupling constant of N=2 supersymmetric Yang-Mills theories can get quantum corrections. Moreover, we prove that all the symmetries defining the theory are algebraically anomaly-free.

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DIAMANDIS, G. A., B. C. GEORGALAS, and N. E. MAVROMATOS. "N=1 SUPERSYMMETRIC SPIN-CHARGE SEPARATION IN EFFECTIVE GAUGE THEORIES OF PLANAR MAGNETIC SUPERCONDUCTORS." Modern Physics Letters A 13, no. 05 (February 20, 1998): 387–404. http://dx.doi.org/10.1142/s0217732398000449.

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We present an N=1 supersymmetric extension of a spin-charge separated effective SU (2)× U S(1) "particle-hole" gauge theory of excitations about the nodes of the gap of a d-wave planar magnetic superconductor. The supersymmetry is achieved without introducing extra degrees of freedom, as compared to the nonsupersymmetric models. The only exception, the introduction of gaugino fields, finds a natural physical interpretation as describing interlayer coupling in the statistical model. The low-energy continuum theory is described by a relativistic (2+1)-dimensional supersymmetric CP1 σ-model with Gross–Neveu–Thirring-type four-fermion interactions. We emphasize the crucial role of the CP1 constraint by inducing a nontrivial dynamical mass generation for fermions (and thus superconductivity), in a way compatible with manifest N=1 supersymmetry. We also give a preliminary discussion of nonperturbative effects. We argue that supersymmetry suppresses the danger of superconductivity instanton contributions to the mass of the perturbatively massless gauge boson of the unbroken U(1) subgroup of SU(2). Finally, we point out the possibility of applying these ideas to effective gauge models of spin-charge separation in one-space dimensional superconducting chains of holons, which, for example, have recently been claimed to be important in the stripe phase of underdoped cuprates.

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Papadopoulos, G. "Supersymmetric Toda field theories." Physics Letters B 365, no. 1-4 (January 1996): 98–104. http://dx.doi.org/10.1016/0370-2693(95)01271-0.

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Evans, Jonathan, and Tim Hollowood. "Supersymmetric Toda field theories." Nuclear Physics B 352, no. 3 (April 1991): 723–68. http://dx.doi.org/10.1016/0550-3213(91)90105-7.

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Elias, V., and D. G. C. McKeon. "The renormalization group with exact β-functions." Canadian Journal of Physics 84, no. 2 (February 1, 2006): 131–43. http://dx.doi.org/10.1139/p06-028.

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The perturbative β-function is known exactly in a number of supersymmetric theories and in the ‘t Hooft renormalization scheme in the [Formula: see text] model. It is shown how this allows one to compute the effective action exactly for certain background field configurations and to relate bare and renormalized couplings. The relationship between the minimal subtraction scheme and the supersymmetry subtraction scheme in N = 1 super YangMills theory is discussed.PACS No.: 11.10Z

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33

KOVACS, STEFANO. "A PERTURBATIVE REANALYSIS OF ${\mathcal N}=4$ SUPERSYMMETRIC YANG–MILLS THEORY." International Journal of Modern Physics A 21, no. 22 (September 10, 2006): 4555–97. http://dx.doi.org/10.1142/s0217751x06031557.

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The finiteness properties of the [Formula: see text] supersymmetric Yang–Mills theory are reanalyzed both in the component formulation and using [Formula: see text] superfields, in order to discuss some subtleties that emerge in the computation of gauge dependent quantities. The one-loop corrections to various Green functions of elementary fields are calculated. In the component formulation it is shown that the choice of the Wess–Zumino gauge, that is standard in supersymmetric gauge theories, introduces ultraviolet divergences in the propagators at the one-loop level. Such divergences are exactly canceled when the contributions of the fields that are put to zero in the Wess–Zumino gauge are taken into account. In the description in terms of [Formula: see text] superfields, infrared divergences are found for every choice of gauge different from the supersymmetric generalization of the Fermi–Feynman gauge. Two-, three- and four-point functions of [Formula: see text] superfields are computed and some general features of the infrared problem are discussed. We also examine the effect of the introduction of mass terms for the (anti)chiral superfields in the theory, which break supersymmetry from [Formula: see text] to [Formula: see text]. It is shown that in the mass deformed model no ultraviolet divergences appear in two-point functions. It is argued that this result can be generalized to n-point functions, supporting the proposal of a possible of use of this modified model as a supersymmetry-preserving regularization scheme for [Formula: see text] theories.

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34

ARNONE, STEFANO, and KENSUKE YOSHIDA. "APPLICATION OF EXACT RENORMALIZATION GROUP TECHNIQUES TO THE NON-PERTURBATIVE STUDY OF SUPERSYMMETRIC FIELD THEORY." International Journal of Modern Physics B 18, no. 04n05 (February 20, 2004): 469–78. http://dx.doi.org/10.1142/s0217979204024082.

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A simple form of the exact renormalization group method is proposed for the study of supersymmetric gauge field theory. The method relies on the existence of ultraviolet-finite four dimensional gauge theories with extended supersymmetry. The resulting exact renormalization group equation crucially depends on the Konishi anomaly of N=1 super Yang–Mills. We illustrate our method by dealing with the NSVZ exact relation for the beta functions, the N=2 super Yang–Mills effective potential and the N=1 super Yang–Mills gluon superpotential (the so-called Veneziano–Yankielowicz potential).

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35

Buchbinder, Ioseph, Evgeny Ivanov, Boris Merzlikin, and Konstantin Stepanyantz. "Harmonic Superspace Approach to the Effective Action in Six-Dimensional Supersymmetric Gauge Theories." Symmetry 11, no. 1 (January 8, 2019): 68. http://dx.doi.org/10.3390/sym11010068.

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We review the recent progress in studying the quantum structure of 6 D , N = ( 1 , 0 ) , and N = ( 1 , 1 ) supersymmetric gauge theories formulated through unconstrained harmonic superfields. The harmonic superfield approach allows one to carry out the quantization and calculations of the quantum corrections in a manifestly N = ( 1 , 0 ) supersymmetric way. The quantum effective action is constructed with the help of the background field method that secures the manifest gauge invariance of the results. Although the theories under consideration are not renormalizable, the extended supersymmetry essentially improves the ultraviolet behavior of the lowest-order loops. The N = ( 1 , 1 ) supersymmetric Yang–Mills theory turns out to be finite in the one-loop approximation in the minimal gauge. Furthermore, some two-loop divergences are shown to be absent in this theory. Analysis of the divergences is performed both in terms of harmonic supergraphs and by the manifestly gauge covariant superfield proper-time method. The finite one-loop leading low-energy effective action is calculated and analyzed. Furthermore, in the Abelian case, we discuss the gauge dependence of the quantum corrections and present its precise form for the one-loop divergent part of the effective action.

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36

CLARK, T. E., C. H. LEE, and S. T. LOVE. "SUPERSYMMETRIC TENSOR GAUGE THEORIES." Modern Physics Letters A 04, no. 14 (July 20, 1989): 1343–53. http://dx.doi.org/10.1142/s0217732389001532.

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The supersymmetric extensions of anti-symmetric tensor gauge theories and their associated tensor gauge symmetry transformations are constructed. The classical equivalence between such supersymmetric tensor gauge theories and supersymmetric non-linear sigma models is established. The global symmetry of the supersymmetric tensor gauge theory is gauged and the locally invariant action is obtained. The supercurrent on the Kähler manifold is found in terms of the supersymmetric tensor gauge field.

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37

FRAMPTON, PAUL H. "SUGGESTION OF EXPLICIT FIELD TRANSFORMATIONS UNDERLYING MISALIGNED SUPERSYMMETRY." Modern Physics Letters A 21, no. 11 (April 10, 2006): 893–97. http://dx.doi.org/10.1142/s0217732306019967.

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In order that nonsupersymmetric quiver gauge theories can satisfy naturalness requirements to all orders of perturbation theory, one expects a global symmetry similar to, but different from, supersymmetry. Consistent with the generalized no-go theorem published by Haag et al. in 1975, we suggest a generalization of supersymmetry to a misaligned supersymmetry where fermionic generators do not commute with gauge transformations. An explicit form for the corresponding field transformations is suggested.

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38

Nozari, Kourosh, F. Moafi, and F. Rezaee Balef. "Some Aspects of Supersymmetric Field Theories with Minimal Length and Maximal Momentum." Advances in High Energy Physics 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/252178.

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We consider a real scalar field and a Majorana fermion field to construct a supersymmetric quantum theory of free fermion fields based on the deformed Heisenberg algebra[x,p] = iℏ(1−βp+2β2p2), whereβis a deformation parameter. We present a deformed supersymmetric algebra in the presence of minimal length and maximal momentum.

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39

McKeon, D. G. C. "One-loop effects in N = 4 supersymmetry." Canadian Journal of Physics 74, no. 3-4 (March 1, 1996): 176–81. http://dx.doi.org/10.1139/p96-028.

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It has been demonstrated that in massless supersymmetric theories, finite radiative corrections to the superpotential can occur (viz. the nonrenormalization theorems can be circumvented). In this paper, we examine the consequences of this in N = 4 supersymmetric Yang–Mills theory, a model in which the β function is known to be zero. It is shown that radiative corrections to the superpotential arise at one loop order in this theory contrary to the expectations of the nonrenormalization theorem, but that their form depends on which formulation of the model is used. When one uses a superfield formulation involving an N = 1 vector superfield and three N = 1 chiral superfields in conjunction with a supersymmetric (but not SU(4)) invariant gauge fixing, then at one-loop order, the radiative generation of terms in the superpotential means that the equality of the gauge and Yukawa couplings and indeed of different Yukawa couplings is lost. If one uses the component field formulation of the N = 4 model in the Wess–Zumino gauge with a covariant, SU(4) invariant (but not supersymmetric invariant) gauge fixing, then the SU(4) invariance is maintained, but the gauge and Yukawa couplings are no longer equal. We also consider computations in the component field formulation in the Wess–Zumino gauge using an N = 1 super Yang–Mills theory in ten dimensions, dimensionally reduced to four dimensions, with a ten-dimensional covariant gauge fixing condition. This formulation ensures that there is no distinction between gauge and Yukawa couplings and that SU(4) invariance is automatically preserved; however, supersymmetry is broken by the gauge fixing procedure.

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40

Addazi, Andrea, and Giampiero Esposito. "Nonlocal quantum field theory without acausality and nonunitarity at quantum level: Is SUSY the key?" International Journal of Modern Physics A 30, no. 15 (May 26, 2015): 1550103. http://dx.doi.org/10.1142/s0217751x15501031.

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The realization of a nonlocal quantum field theory without losing unitarity, gauge invariance and causality is investigated. It is commonly retained that such a formulation is possible at tree level, but at quantum level acausality is expected to reappear at one loop. We suggest that the problem of acausality is, in a broad sense, similar to the one about anomalies in quantum field theory. By virtue of this analogy, we suggest that acausal diagrams resulting from the fermionic sector and the bosonic one might cancel each other, with a suitable content of fields and suitable symmetries. As a simple example, we show how supersymmetry can alleviate this problem in a simple and elegant way, i.e. by leading to exact cancellations of harmful diagrams, to all orders of perturbation theory. An infinite number of divergent diagrams cancel each other by virtue of the nonrenormalization theorem of supersymmetry. However, supersymmetry is not enough to protect a theory from all acausal divergences. For instance, acausal contributions to supersymmetric corrections to D-terms are not protected by supersymmetry. On the other hand, we show in detail how supersymmetry also helps in dealing with D-terms: divergences are not canceled but they become softer than in the nonsupersymmetric case. The supergraphs' formalism turns out to be a powerful tool to reduce the complexity of perturbative calculations.

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41

INTRILIGATOR, KENNETH. "ASPECTS OF SUPERSYMMETRIC FIELD THEORIES." International Journal of Modern Physics A 25, no. 02n03 (January 30, 2010): 391–400. http://dx.doi.org/10.1142/s0217751x1004869x.

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42

Argyres, Philip C. "Dualities in supersymmetric field theories." Nuclear Physics B - Proceedings Supplements 61, no. 1-2 (February 1998): 149–57. http://dx.doi.org/10.1016/s0920-5632(97)00527-6.

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43

Warner, N. P. "Supersymmetric, integrable boundary field theories." Nuclear Physics B - Proceedings Supplements 45, no. 1 (January 1996): 154–63. http://dx.doi.org/10.1016/0920-5632(95)00625-7.

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44

Kogut, John B. "Simulating simple supersymmetric field theories." Physics Letters B 187, no. 3-4 (March 1987): 347–50. http://dx.doi.org/10.1016/0370-2693(87)91107-5.

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45

KETOV, SERGEI V. "THE OSp(32|1) VERSUS OSp(8|2) SUPERSYMMETRIC M-BRANE ACTION FROM SELF-DUAL (2, 2) STRINGS." Modern Physics Letters A 11, no. 29 (September 21, 1996): 2369–79. http://dx.doi.org/10.1142/s0217732396002368.

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Taking the (2, 2) strings as a starting point, we discuss the equivalent integrable field theories and analyze their symmetry structure in 2+2 dimensions from the viewpoint of string/membrane unification. Requiring the “Lorentz” invariance and supersymmetry in the (2, 2) string target space leads to an extension of the (2, 2) string theory to a theory of (2+2)-dimensional supermembranes (M-branes) propagating in a higher-dimensional target space. The origin of the hidden target space dimensions of the M-brane is related to the maximally extended supersymmetry implied by the “Lorentz” covariance and dimensional reasons. The Kähler-Chern-Simons-type action describing the self-dual gravity in 2+2 dimensions is proposed. Its maximal supersymmetric extension (of the Green-Schwarz-type) naturally leads to the 2+10 (or higher) dimensions for the M-brane target space. The proposed OSp (32|1) supersymmetric action gives the pre-geometrical description of M-branes, which may be useful for a fundamental formulation of F&M theory.

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Kazakov, Dmitry, Leonid Bork, Arthur Borlakov, Denis Tolkachev, and Dmitry Vlasenko. "High Energy Behavior in Maximally Supersymmetric Gauge Theories in Various Dimensions." Symmetry 11, no. 1 (January 17, 2019): 104. http://dx.doi.org/10.3390/sym11010104.

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Maximally supersymmetric field theories in various dimensions are believed to possess special properties due to extended supersymmetry. In four dimensions, they are free from UV divergences but are IR divergent on shell; in higher dimensions, on the contrary, they are IR finite but UV divergent. In what follows, we consider the four-point on-shell scattering amplitudes in D = 6 , 8 , 10 supersymmetric Yang–Mills theory in the planar limit within the spinor-helicity and on-shell supersymmetric formalism. We study the UV divergences and demonstrate how one can sum them over all orders of PT. Analyzing the R -operation, we obtain the recursive relations and derive differential equations that sum all leading, subleading, etc., divergences in all loops generalizing the standard RG formalism for the case of nonrenormalizable interactions. We then perform the renormalization procedure, which differs from the ordinary one in that the renormalization constant becomes the operator depending on kinematics. Solving the obtained RG equations for particular sets of diagrams analytically and for the general case numerically, we analyze their high energy behavior and find that, while each term of PT increases as a power of energy, the total sum behaves differently: in D = 6 two partial amplitudes decrease with energy and the third one increases exponentially, while in D = 8 and 10 the amplitudes possess an infinite number of periodic poles at finite energy.

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47

Lü, H., and C. N. Pope. "Multiscalar p-Brane Solitons." International Journal of Modern Physics A 12, no. 02 (January 20, 1997): 437–50. http://dx.doi.org/10.1142/s0217751x97000499.

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In a previous paper,10 supersymmetric p-brane solutions involving one dilatonic scalar field in maximal supergravity theories were classified. Although these solutions involve a number of participating field strengths, they are all equal and thus they carry equal electric or magnetic charges. In this paper, we generalize all these solutions to multiscalar solutions in which the charges become independent free parameters. The mass per unit p volume is equal to the sum of these Page charges. We find that for generic values of the Page charges, they preserve the same fraction of the supersymmetry as in their single scalar limits.

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IVANOV, E. A., and A. A. KAPUSTNIKOV. "GAUGE-COVARIANT WESS-ZUMINO ACTIONS FOR SUPER p-BRANES IN SUPERSPACE." International Journal of Modern Physics A 07, no. 10 (April 20, 1992): 2153–73. http://dx.doi.org/10.1142/s0217751x92000958.

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We present a general method of constructing manifestly world-volume supersymmetric actions of super p-branes, starting from some higher-dimensional field theories in which the partial breaking of global supersymmetry (PBGS) comes about. Our approach is based upon a substitution of the superspace coordinates which relates linear and nonlinear realizations of PBGS. As instructive examples we consider the massive d=2 superparticle (p=0) and d=4 superstring (p=1). The relevant world-line and world-sheet superfied actions naturally appear as a long-wavelength limit of the superfield actions of some two- and four-dimensional supersymmetric field theories possessing topologically nontrivial soliton solutions. The corresponding topological charges prove to enter the super p-brane actions as the coupling constants. We also give a new general Wess-Zumino-type representation of the d=2 superparticle action via the world-line superfields. It respects invariances both under the target space Poincaré supersymmetry and the gauge group of general reparametrizations of the world-line superspace. In one gauge, it is reduced to the standard PBGS form while in another, it gives rise to a very simple action which displays manifest world-line superconformal symmetry and is directly related to the familiar component action of the superparticle. The fermionic κ-symmetry of the latter can be identified with the odd sector of superconformal symmetry. This identity suggests a simple recipe for building higher-order κ-invariant corrections to the minimal superparticle action.

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49

Álvarez, Gustavo, Gorazd Cvetič, Bernd A. Kniehl, Igor Kondrashuk, and Ivan Parra-Ferrada. "Analytical Solution to DGLAP Integro-Differential Equation in a Simple Toy-Model with a Fixed Gauge Coupling." Quantum Reports 5, no. 1 (February 27, 2023): 198–223. http://dx.doi.org/10.3390/quantum5010013.

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We consider a simple model for QCD dynamics in which DGLAP integro-differential equation may be solved analytically. This is a gauge model which possesses dominant evolution of gauge boson (gluon) distribution and in which the gauge coupling does not run. This may be N=4 supersymmetric gauge theory with softly broken supersymmetry, other finite supersymmetric gauge theory with a lower level of supersymmetry, or topological Chern–Simons field theories. We maintain only one term in the splitting function of unintegrated gluon distribution and solve DGLAP analytically for this simplified splitting function. The solution is found using the Cauchy integral formula. The solution restricts the form of the unintegrated gluon distribution as a function of momentum transfer and of Bjorken x. Then, we consider an almost realistic splitting function of unintegrated gluon distribution as an input to DGLAP equation and solve it by the same method which we have developed to solve DGLAP equation for the toy-model. We study a result obtained for the realistic gluon distribution and find a singular Bessel-like behavior in the vicinity of the point x=0 and a smooth behavior in the vicinity of the point x=1.

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BLAU, MATTHIAS. "CHERN-SIMONS QUANTUM MECHANICS, SUPERSYMMETRY, AND SYMPLECTIC INVARIANTS." International Journal of Modern Physics A 06, no. 03 (January 30, 1991): 365–79. http://dx.doi.org/10.1142/s0217751x91000228.

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We explain the relation between supersymmetry and equivariant cohomology, combining recent investigations of Chern-Simons quantum mechanics and path integrals on coadjoint orbits. We then construct a supersymmetric (topological) quantum mechanics model whose partition function — probing the cohomology of the symplectomorphism group — yields a symplectic invariant introduced by Weinstein. We demonstrate by explicit calculation that this provides another example where the Duistermaat-Heckman theorem (exactness of the semi-classical approximation) appears to hold in infinite dimensions, and make some suggestions concerning its role in (conformal) field theory.

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