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34 pages, 684 KiB

Open AccessArticle

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 2553

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 \times 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

Open AccessArticle

Generating All 36,864 Four-Color Adinkras via Signed Permutations and Organizing into ℓ- and ℓ ˜ -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 3679

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

Open AccessFeature PaperArticle

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 2918

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

Open AccessArticle

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 - 8 Jan 2019

Cited by 9 | Viewed by 3193

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

Open AccessArticle

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 2642

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

Open AccessFeature PaperArticle

Vacuum Constraints for Realistic Strongly Coupled Heterotic M-Theories

by Burt A. Ovrut

Symmetry 2018, 10(12), 723; https://doi.org/10.3390/sym10120723 - 5 Dec 2018

Cited by 13 | Viewed by 2168

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

Jump to: Research

18 pages, 409 KiB

Open AccessEditor’s ChoiceReview

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 - 9 Apr 2019

Cited by 40 | Viewed by 3685

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

Open AccessFeature PaperReview

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 2463

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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