Статті в журналах: "Rigid Supersymmetric Theory"

1

Kulshreshtha, Daya Shankar, and Usha Kulshreshtha. "On the Wess-Zumino Model: a supersymmetric field theory." Acta Polytechnica 62, no. 1 (February 28, 2022): 80–84. http://dx.doi.org/10.14311/ap.2022.62.0080.

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We consider the free massless Wess-Zumino Model in 4D which describes a supersymmetric field theory that is invariant under the rigid or global supersymmetry transformations where the transformation parameter ϵ (or ϵ ) is a constant Grassmann spinor. We quantize the theory using the Hamiltonian and path integral formulations.

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2

Upadhyay, Sudhaker. "Spontaneous breaking of nilpotent symmetry in boundary BLG theory." International Journal of Modern Physics A 30, no. 25 (September 9, 2015): 1550150. http://dx.doi.org/10.1142/s0217751x1550150x.

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We exploit boundary term to preserve the supersymmetric gauge invariance of Bagger–Lambert–Gustavsson (BLG) theory. The fermionic rigid BRST and anti-BRST symmetries are studied in linear and nonlinear gauges. Remarkably, for Delbourgo–Jarvis–Baulieu–Thierry–Mieg (DJBTM) type gauge the spontaneous breaking of BRST symmetry occurs in the BLG theory. The responsible guy for such spontaneous breaking is ghost–antighost condensation. Further, we discuss the ghost–antighost condensates in the modified maximally Abelian (MMA) gauge in the BLG theory.

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3

PIGUET, O., and K. SIBOLD. "NONRENORMALIZATION THEOREMS OF CHIRAL ANOMALIES AND FINITENESS IN SUPERSYMMETRIC YANG-MILLS THEORIES." International Journal of Modern Physics A 01, no. 04 (December 1986): 913–42. http://dx.doi.org/10.1142/s0217751x86000332.

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We prove a generalized nonrenormalization theorem for U(1) axial anomalies in rigid N=1 supersymmetric gauge theories in 4 space-time dimensions. The theorem implies one-loop criteria for β-functions vanishing to all orders of perturbation theory. The criteria are applicable to all N=1 theories with simple gauge group.

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4

FEICHTINGER, U., O. MORITSCH, J. RANT, M. SCHWEDA, and H. ZERROUKI. "THE FINITENESS OF THE FOUR-DIMENSIONAL ANTISYMMETRIC TENSOR FIELD MODEL IN A CURVED BACKGROUND." International Journal of Modern Physics A 13, no. 26 (October 20, 1998): 4513–37. http://dx.doi.org/10.1142/s0217751x98002171.

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A renormalizable rigid supersymmetry for the four-dimensional antisymmetric tensor field model in a curved space–time background is constructed. A closed algebra between the BRS and the supersymmetry operators is only realizable if the vector parameter of the supersymmetry is a covariantly constant vector field. This also guarantees that the corresponding transformations lead to a genuine symmetry of the model. The proof of the ultraviolet finiteness to all orders of perturbation theory is performed in a pure algebraic manner by using the rigid supersymmetry.

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5

Nekrasov, Nikita, Nicolo Piazzalunga, and Maxim Zabzine. "Shifts of prepotentials (with an appendix by Michele Vergne)." SciPost Physics 12, no. 5 (May 27, 2022). http://dx.doi.org/10.21468/scipostphys.12.5.177.

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We study the dynamics of supersymmetric theories in five dimensions obtained by compactifications of M-theory on a Calabi-Yau threefold X. For a compact X, this is determined by the geometry of X, in particular the Kähler class dependence of the volume of X determines the effective couplings of vector multiplets. Rigid supersymmetry emerges in the limit of divergent volume, prompting the study of the structure of Duistermaat-Heckman formula and its generalizations for non-compact toric Kähler manifolds. Our main tool is the set of finite-difference equations obeyed by equivariant volumes and their quantum versions. We also discuss a physical application of these equations in the context of seven-dimensional gauge theories, extending and clarifying our previous results. The appendix by M. Vergne provides an alternative local proof of the shift equation.

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6

Bardzell, Jacob, Eduardo Gonzalo, Muthusamy Rajaguru, Danielle Smith, and Timm Wrase. "Type IIB flux compactifications with h1,1 = 0." Journal of High Energy Physics 2022, no. 6 (June 2022). http://dx.doi.org/10.1007/jhep06(2022)166.

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Abstract We revisit flux compactifications of type IIB string theory on ‘spaces’ dual to rigid Calabi-Yau manifolds. This rather unexplored part of the string landscapes harbors many interesting four-dimensional solutions, namely supersymmetric $$ \mathcal{N} $$ N = 1 Minkowski vacua without flat direction and infinite families of AdS vacua, some potentially with unrestricted rank for the gauge group. We also comment on the existence of metastable dS solutions in this setup. We discuss how these solutions fit into the web of swampland conjectures.

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7

Ding, Gui-Jun, Ferruccio Feruglio, and Xiang-Gan Liu. "Automorphic forms and fermion masses." Journal of High Energy Physics 2021, no. 1 (January 2021). http://dx.doi.org/10.1007/jhep01(2021)037.

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Abstract We extend the framework of modular invariant supersymmetric theories to encompass invariance under more general discrete groups Γ, that allow the presence of several moduli and make connection with the theory of automorphic forms. Moduli span a coset space G/K, where G is a Lie group and K is a compact subgroup of G, modded out by Γ. For a general choice of G, K, Γ and a generic matter content, we explicitly construct a minimal Kähler potential and a general superpotential, for both rigid and local $$ \mathcal{N} $$ N = 1 supersymmetric theories. We also specialize our construction to the case G = Sp(2g, ℝ), K = U(g) and Γ = Sp(2g, ℤ), whose automorphic forms are Siegel modular forms. We show how our general theory can be consistently restricted to multi-dimensional regions of the moduli space enjoying residual symmetries. After choosing g = 2, we present several examples of models for lepton and quark masses where Yukawa couplings are Siegel modular forms of level 2.

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8

Ding, Gui-Jun, Ferruccio Feruglio, and Xiang-Gan Liu. "Automorphic forms and fermion masses." Journal of High Energy Physics 2021, no. 1 (January 2021). http://dx.doi.org/10.1007/jhep01(2021)037.

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Анотація:

Abstract We extend the framework of modular invariant supersymmetric theories to encompass invariance under more general discrete groups Γ, that allow the presence of several moduli and make connection with the theory of automorphic forms. Moduli span a coset space G/K, where G is a Lie group and K is a compact subgroup of G, modded out by Γ. For a general choice of G, K, Γ and a generic matter content, we explicitly construct a minimal Kähler potential and a general superpotential, for both rigid and local $$ \mathcal{N} $$ N = 1 supersymmetric theories. We also specialize our construction to the case G = Sp(2g, ℝ), K = U(g) and Γ = Sp(2g, ℤ), whose automorphic forms are Siegel modular forms. We show how our general theory can be consistently restricted to multi-dimensional regions of the moduli space enjoying residual symmetries. After choosing g = 2, we present several examples of models for lepton and quark masses where Yukawa couplings are Siegel modular forms of level 2.

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9

Ishiguro, Keiya, and Hajime Otsuka. "Sharpening the boundaries between flux landscape and swampland by tadpole charge." Journal of High Energy Physics 2021, no. 12 (December 2021). http://dx.doi.org/10.1007/jhep12(2021)017.

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Abstract We investigate the vacuum structure of four-dimensional effective theory arising from Type IIB flux compactifications on a mirror of the rigid Calabi-Yau threefold, corresponding to a T-dual of the DeWolfe-Giryavets-Kachru-Taylor model in Type IIA flux compactifications. By analyzing the vacuum structure of this interesting corner of string landscape, it turns out that there exist perturbatively unstable de Sitter (dS) vacua in addition to supersymmetric and non-supersymmetric anti-de Sitter vacua. On the other hand, the stable dS vacua appearing in the low-energy effective action violate the tadpole cancellation condition, indicating a strong correlation between the existence of dS vacua and the flux-induced D3-brane charge (tadpole charge). We also find analytically that the tadpole charge constrained by the tadpole cancellation condition emerges in the scalar potential in a nontrivial way. Thus, the tadpole charge would restrict the existence of stable dS vacua, and this fact underlies the statement of the dS conjecture. Furthermore, our analytical and numerical results exhibit that distributions of $$ \mathcal{O}(1) $$ O 1 parameters in expressions of several swampland conjectures peak at specific values.

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10

Kuzenko, Sergei M., Ulf Lindström, Emmanouil S. N. Raptakis, and Gabriele Tartaglino-Mazzucchelli. "Symmetries of $$ \mathcal{N} $$ = (1, 0) supergravity backgrounds in six dimensions." Journal of High Energy Physics 2021, no. 3 (March 2021). http://dx.doi.org/10.1007/jhep03(2021)157.

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Abstract General $$ \mathcal{N} $$ N = (1, 0) supergravity-matter systems in six dimensions may be described using one of the two fully fledged superspace formulations for conformal supergravity: (i) SU(2) superspace; and (ii) conformal superspace. With motivation to develop rigid supersymmetric field theories in curved space, this paper is devoted to the study of the geometric symmetries of supergravity backgrounds. In particular, we introduce the notion of a conformal Killing spinor superfield ϵα, which proves to generate extended superconformal transformations. Among its cousins are the conformal Killing vector ξa and tensor ζa(n) superfields. The former parametrise conformal isometries of supergravity backgrounds, which in turn yield symmetries of every superconformal field theory. Meanwhile, the conformal Killing tensors of a given background are associated with higher symmetries of the hypermultiplet. By studying the higher symmetries of a non-conformal vector multiplet we introduce the concept of a Killing tensor superfield. We also analyse the problem of computing higher symmetries for the conformal d’Alembertian in curved space and demonstrate that, beyond the first-order case, these operators are defined only on a limited class of backgrounds, including all conformally flat ones.

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11

Cecotti, Sergio. "Special geometry and the swampland." Journal of High Energy Physics 2020, no. 9 (September 2020). http://dx.doi.org/10.1007/jhep09(2020)147.

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Abstract In the context of 4d effective gravity theories with 8 supersymmetries, we propose to unify, strenghten, and refine the several swampland conjectures into a single statement: the structural criterion, modelled on the structure theorem in Hodge theory. In its most abstract form the new swampland criterion applies to all 4d $$ \mathcal{N} $$ N = 2 effective theories (having a quantum-consistent UV completion) whether supersymmetry is local or rigid: indeed it may be regarded as the more general version of Seiberg-Witten geometry which holds both in the rigid and local cases.As a first application of the new swampland criterion we show that a quantum-consistent $$ \mathcal{N} $$ N = 2 supergravity with a cubic pre-potential is necessarily a truncation of a higher-$$ \mathcal{N} $$ N sugra. More precisely: its moduli space is a Shimura variety of ‘magic’ type. In all other cases a quantum-consistent special Kähler geometry is either an arithmetic quotient of the complex hyperbolic space SU(1, m)/U(m) or has no local Killing vector.Applied to Calabi-Yau 3-folds this result implies (assuming mirror symmetry) the validity of the Oguiso-Sakurai conjecture in Algebraic Geometry: all Calabi-Yau 3-folds X without rational curves have Picard number ρ = 2, 3; in facts they are finite quotients of Abelian varieties. More generally: the Kähler moduli of X do not receive quantum corrections if and only if X has infinite fundamental group. In all other cases the Kähler moduli have instanton corrections in (essentially) all possible degrees.

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12

Akhond, Mohammad, Guillermo Arias Tamargo, Alessandro Mininno, Hao-Yu Sun, Zhengdi Sun, Yifan Wang, and Fengjun Xu. "The hitchhiker's guide to 4d $\mathcal{N}=2$ superconformal field theories." SciPost Physics Lecture Notes, October 26, 2022. http://dx.doi.org/10.21468/scipostphyslectnotes.64.

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Superconformal field theory with \mathcal{N}=2𝒩=2 supersymmetry in four dimensional spacetime provides a prime playground to study strongly coupled phenomena in quantum field theory. Its rigid structure ensures valuable analytic control over non-perturbative effects, yet the theory is still flexible enough to incorporate a large landscape of quantum systems. Here we aim to offer a guidebook to fundamental features of the 4d \mathcal{N}=2𝒩=2 superconformal field theories and basic tools to construct them in string/M-/F-theory. The content is based on a series of lectures at the Quantum Field Theories and Geometry School in July 2020.

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13

Bossard, Guillaume, Axel Kleinschmidt, and Ergin Sezgin. "A master exceptional field theory." Journal of High Energy Physics 2021, no. 6 (June 2021). http://dx.doi.org/10.1007/jhep06(2021)185.

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Abstract We construct a pseudo-Lagrangian that is invariant under rigid E11 and transforms as a density under E11 generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on E11 exceptional field theory and the inclusion of constrained fields that transform in an indecomposable E11-representation together with the E11 coset fields. We show that, in combination with gauge-invariant and E11-invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condi- tion. For another choice, we reobtain the E8 exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the E10 sigma model.

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14

El Kinani, M. N., and M. Vall. "On the partial breaking of $\mathcal{N}=2$ rigid supersymmetry with a complex hypermultiplet." Progress of Theoretical and Experimental Physics 2019, no. 12 (December 1, 2019). http://dx.doi.org/10.1093/ptep/ptz145.

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Abstract We study partial supersymmetry breaking in effective $\mathcal{N}=2$ U$ \left( 1\right) ^{n}$ gauge theory coupled to complex hypermultiplets by using the method of L. Andrianopoli et al., Phys. Lett. B 744, 116 (2015), which we refer to as the ADFT method. We derive the generalization of the symplectic invariant ADFT formula $\zeta _{a}=\frac{1}{2}\varepsilon _{abc}(\mathcal{P}^{bM}\mathcal{C}_{MN}\mathcal{P}^{cN}) $, capturing information on partial breaking. Our extension of this anomaly is expressed as $d_{a}=\frac{1}{2}\varepsilon _{abc}\mathbb{P}^{bM}\mathcal{C}_{MN}\mathbb{P}^{cN}+\mathcal{J}_{a}$. The generalized moment maps $\mathbb{P}^{aM}$ contain $\mathcal{P}^{aM}$ and also depend on electric/magnetic coupling charges $G^{M}=( \eta ^{i},g_{i}) $; the $\mathcal{J}_{a}$ is an extra contribution induced by Killing isometries in the complex hypermatter sector. Using SP$\left(2n,\mathbb{R}\right)$ symplectic symmetry, we also give the $\mathcal{N}=2$ partial breaking condition and derive the model of I. Antoniadis et al., Nucl. Phys. B 863, 471 (2012) by a particular realization of the $d_{a}$ anomaly.

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15

Tsuda, Motomu. "On commutator-based linearization of vector-spinor nonlinear supersymmetry and Rarita–Schwinger fields." Modern Physics Letters A 37, no. 29 (September 21, 2022). http://dx.doi.org/10.1142/s0217732322501978.

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In this paper, we discuss the linearization of vector-spinor (spin-3/2) nonlinear supersymmetry (vsNLSUSY) transformations for both [Formula: see text] and [Formula: see text]-extended SUSY in flat spacetime based on the commutator algebra by using functionals (composites) of spin-3/2 Nambu–Goldstone (NG) fermions, which are expressed as simple products of powers of the spin-3/2 NG fermions and a fundamental determinant in the vsNLSUSY theory. We define basic component fields by means of those functionals in a linearized vsSUSY theory including spin-3/2 fields, general auxiliary ones and a [Formula: see text]-term. The general forms of linear (rigid) vsSUSY transformations for the component fields are determined uniquely from the commutator-based linearization procedure. By considering appropriate recombinations of the functionals of the spin-3/2 NG fermions for [Formula: see text] SUSY, we find that variations of the recombinations under the vsNLSUSY transformations include linear spin-1/2 SUSY ones of spin-[Formula: see text] fields with [Formula: see text] gauge invariance. The spinorial gauge invariance of the Rarita–Schwinger action in the linearization process is also discussed together with the [Formula: see text] gauge invariance.

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Статті в журналах з теми "Rigid Supersymmetric Theory"

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