Supersymmetric Field Theory 2018

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: closed (31 January 2019) | Viewed by 21092

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Guest Editor
Department of Theoretical Physics, Tomsk State Pedagogical University, Kiyevskaya Ulitsa, 60А, Tomskaya Oblast', 634061 Tomsk, Russia
Interests: quantum filed theory; quantum gravity; supersymmetry and supergravity; string theory; higher spin field theory

Special Issue Information

Dear Colleagues,

This Special Issue, “Supersymmetric Field Theory 2018”, will be devoted to current problems of classical and quantum supersymmetric field theory. At present, studies of the various aspects supersymmetry in physics and mathematics are actively developing research areas. Supersymmetry as an extension of the space–time symmetries is very broadly used in higher energy physics to describe the possible phenomena beyond the standard model of elementary particles. Use of supersymmetry in gravity allows us to construct new gravitational models with remarkable properties that, in turn, lead to possible interesting cosmological applications. Supersymmetry in quantum field theory provides a cancellation of some of the possible ultraviolet divergences and permits to formulate completely finite quantum filled models like the N=4 super Yang-Mills theory.  In addition, supersymmetry is an element of superstring theory.  Additionally, we point out that specific BRST supersymmetry underlies the modern approaches to quantization of gauge theories. This Special Issue will focus on selected active research directions of modern supersymmetric field theory.

Main topics include:

  • Formulation of the new supersymmetric models in various dimensions
  • Study a quantum structure of supersymmetric gauge theories
  • Superspace methods in supersymmetric field models
  • Problem of ultraviolet divergences in higher dimensional supersymmetric models
  • Supersymmetric extension of the standard model
  • Mathematical aspects of supersymmetric field theories

Additionally, the Special Issue is open to related topics.

Prof. Dr. Joseph L. Buchbinder
Guest Editors

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Keywords

  • Supersymmetry
  • Superalgebra
  • Superfield
  • Effective action
  • Gauge theory
  • Quantization
  • Divergences and renormalizations
  • Yang-Mills theory
  • Chern-Simons theory
  • Supergravity
  • Higher dimensions

Published Papers (8 papers)

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Research

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34 pages, 684 KiB  
Article
4D, N = 1 Matter Gravitino Genomics
by S.-N. Hazel Mak and Kory Stiffler
Symmetry 2019, 11(2), 217; https://doi.org/10.3390/sym11020217 - 13 Feb 2019
Cited by 1 | Viewed by 2281
Abstract
Adinkras are graphs that encode a supersymmetric representation’s transformation laws that have been reduced to one dimension, that of time. A goal of the supersymmetry “genomics” project is to classify all 4D, N = 1 off-shell supermultiplets in terms of their adinkras. In [...] Read more.
Adinkras are graphs that encode a supersymmetric representation’s transformation laws that have been reduced to one dimension, that of time. A goal of the supersymmetry “genomics” project is to classify all 4D, N = 1 off-shell supermultiplets in terms of their adinkras. In previous works, the genomics project uncovered two fundamental isomer adinkras, the cis- and trans-adinkras, into which all multiplets investigated to date can be decomposed. The number of cis- and trans-adinkras describing a given multiplet define the isomer-equivalence class to which the multiplet belongs. A further refining classification is that of a supersymmetric multiplet’s holoraumy: the commutator of the supercharges acting on the representation. The one-dimensionally reduced, matrix representation of a multiplet’s holoraumy defines the multiplet’s holoraumy-equivalence class. Together, a multiplet’s isomer-equivalence and holoraumy-equivalence classes are two of the main characteristics used to distinguish the adinkras associated with different supersymmetry multiplets in higher dimensions. This paper focuses on two matter gravitino formulations, each with 20 bosonic and 20 fermionic off-shell degrees of freedom, analyzes them in terms of their isomer- and holoraumy-equivalence classes, and compares with non-minimal supergravity which is also a 20 × 20 multiplet. This analysis fills a missing piece in the supersymmetry genomics project, as now the isomer-equivalence and holoraumy-equivalence for representations up to spin two in component fields have been analyzed for 4D, N = 1 supersymmetry. To handle the calculations of this research effort, we have used the Mathematica software package called Adinkra.m. This package is open-source and available for download at a GitHub Repository. Data files associated with this paper are also published open-source at a Data Repository also on GitHub. Full article
(This article belongs to the Special Issue Supersymmetric Field Theory 2018)
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42 pages, 566 KiB  
Article
Generating All 36,864 Four-Color Adinkras via Signed Permutations and Organizing into - and ˜ -Equivalence Classes
by S. James Gates, Jr., Kevin Iga, Lucas Kang, Vadim Korotkikh and Kory Stiffler
Symmetry 2019, 11(1), 120; https://doi.org/10.3390/sym11010120 - 20 Jan 2019
Cited by 7 | Viewed by 3174
Abstract
Recently, all 1,358,954,496 values of the gadget between the 36,864 adinkras with four colors, four bosons, and four fermions have been computed. In this paper, we further analyze these results in terms of B C 3 , the signed permutation group of three [...] Read more.
Recently, all 1,358,954,496 values of the gadget between the 36,864 adinkras with four colors, four bosons, and four fermions have been computed. In this paper, we further analyze these results in terms of B C 3 , the signed permutation group of three elements, and B C 4 , the signed permutation group of four elements. It is shown how all 36,864 adinkras can be generated via B C 4 boson × B C 3 color transformations of two quaternion adinkras that satisfy the quaternion algebra. An adinkra inner product has been used for some time, known as the gadget, which is used to distinguish adinkras. We show how 96 equivalence classes of adinkras that are based on the gadget emerge in terms of B C 3 and B C 4 . We also comment on the importance of the gadget as it relates to separating out dynamics in terms of Kähler-like potentials. Thus, on the basis of the complete analysis of the supersymmetrical representations achieved in the preparatory first four sections, the final comprehensive achievement of this work is the construction of the universal B C 4 non-linear σ -model. Full article
(This article belongs to the Special Issue Supersymmetric Field Theory 2018)
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29 pages, 9021 KiB  
Article
High Energy Behavior in Maximally Supersymmetric Gauge Theories in Various Dimensions
by Dmitry Kazakov, Leonid Bork, Arthur Borlakov, Denis Tolkachev and Dmitry Vlasenko
Symmetry 2019, 11(1), 104; https://doi.org/10.3390/sym11010104 - 17 Jan 2019
Cited by 4 | Viewed by 2570
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Supersymmetric Field Theory 2018)
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28 pages, 854 KiB  
Article
Harmonic Superspace Approach to the Effective Action in Six-Dimensional Supersymmetric Gauge Theories
by Ioseph Buchbinder, Evgeny Ivanov, Boris Merzlikin and Konstantin Stepanyantz
Symmetry 2019, 11(1), 68; https://doi.org/10.3390/sym11010068 - 08 Jan 2019
Cited by 9 | Viewed by 2822
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Supersymmetric Field Theory 2018)
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10 pages, 306 KiB  
Article
Modified Born–Infeld-Dilaton-Axion Coupling in Supersymmetry
by Yermek Aldabergenov and Sergei V. Ketov
Symmetry 2019, 11(1), 14; https://doi.org/10.3390/sym11010014 - 24 Dec 2018
Cited by 2 | Viewed by 2353
Abstract
We propose the supersymmetric extension of the modified Born–Infeld-axion-dilaton non-linear electrodynamics that has confined static abelian solutions used for describing the electromagnetic confinement in the presence of axion and dilaton fields, as well as charged matter. The supersymmetric extension also has the non-trivial [...] Read more.
We propose the supersymmetric extension of the modified Born–Infeld-axion-dilaton non-linear electrodynamics that has confined static abelian solutions used for describing the electromagnetic confinement in the presence of axion and dilaton fields, as well as charged matter. The supersymmetric extension also has the non-trivial scalar potential that implies the upper bounds on the matter fields. Full article
(This article belongs to the Special Issue Supersymmetric Field Theory 2018)
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22 pages, 556 KiB  
Article
Vacuum Constraints for Realistic Strongly Coupled Heterotic M-Theories
by Burt A. Ovrut
Symmetry 2018, 10(12), 723; https://doi.org/10.3390/sym10120723 - 05 Dec 2018
Cited by 13 | Viewed by 1875
Abstract
The compactification from the 11-dimensional Horava-Witten orbifold to 5-dimensional heterotic M-theory on a Schoen Calabi-Yau threefold is reviewed, as is the specific S U ( 4 ) vector bundle leading to the “heterotic standard model” in the observable sector. A generic formalism for [...] Read more.
The compactification from the 11-dimensional Horava-Witten orbifold to 5-dimensional heterotic M-theory on a Schoen Calabi-Yau threefold is reviewed, as is the specific S U ( 4 ) vector bundle leading to the “heterotic standard model” in the observable sector. A generic formalism for a consistent hidden sector gauge bundle, within the context of strongly coupled heterotic M-theory, is presented. Anomaly cancellation and the associated bulk space 5-branes are discussed in this context. The further compactification to a 4-dimensional effective field theory on a linearized BPS double domain wall is then presented to order κ 11 4 / 3 . Specifically, the generic constraints required for anomaly cancellation and by the linearized domain wall solution, restrictions imposed by the vanishing of the D-terms and, finally, the constraints imposed by the necessity for positive, perturbative squared gauge couplings to this order are presented in detail. Full article
(This article belongs to the Special Issue Supersymmetric Field Theory 2018)
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Review

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18 pages, 409 KiB  
Review
Cosmological Probes of Supersymmetric Field Theory Models at Superhigh Energy Scales
by Sergei V. Ketov and Maxim Yu. Khlopov
Symmetry 2019, 11(4), 511; https://doi.org/10.3390/sym11040511 - 09 Apr 2019
Cited by 39 | Viewed by 3178
Abstract
The lack of positive results in searches for supersymmetric (SUSY) particles at the Large Hadron Collider (LHC) and in direct searches for Weakly Interacting Massive Particles (WIMPs) in the underground experiments may hint to a super-high energy scale of SUSY phenomena beyond the [...] Read more.
The lack of positive results in searches for supersymmetric (SUSY) particles at the Large Hadron Collider (LHC) and in direct searches for Weakly Interacting Massive Particles (WIMPs) in the underground experiments may hint to a super-high energy scale of SUSY phenomena beyond the reach of direct experimental probes. At such scales the supergravity models based on Starobinsky inflation can provide the mechanisms for both inflation and superheavy dark matter. However, it makes the indirect methods the only way of testing the SUSY models, so that cosmological probes acquire the special role in this context. Such probes can rely on the nontrivial effects of SUSY physics in the early Universe, which are all model-dependent and thus can provide discrimination of the models and their parameters. The nonstandard cosmological features like Primordial Black Holes (PBHs) or antimatter domains in a baryon-asymmetric universe are discussed as possible probes for high energy scale SUSY physics. Full article
(This article belongs to the Special Issue Supersymmetric Field Theory 2018)
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11 pages, 760 KiB  
Review
Deformed N = 8 Supersymmetric Mechanics
by Evgeny Ivanov, Olaf Lechtenfeld and Stepan Sidorov
Symmetry 2019, 11(2), 135; https://doi.org/10.3390/sym11020135 - 26 Jan 2019
Cited by 4 | Viewed by 2105
Abstract
We give a brief review of deformed N = 8 supersymmetric mechanics as a generalization of SU(2|1) mechanics. It is based on the worldline realizations of the supergroups SU(2|2) and SU(4|1) in the appropriate N = 8 , d = 1 superspaces. The [...] Read more.
We give a brief review of deformed N = 8 supersymmetric mechanics as a generalization of SU(2|1) mechanics. It is based on the worldline realizations of the supergroups SU(2|2) and SU(4|1) in the appropriate N = 8 , d = 1 superspaces. The corresponding models are deformations of the standard N = 8 mechanics models by a mass parameter m. Full article
(This article belongs to the Special Issue Supersymmetric Field Theory 2018)
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