Symmetry

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12 pages, 434 KiB

Open AccessArticle

Heisenberg Parabolic Subgroups of Exceptional Non-Compact G₂₍₂₎ and Invariant Differential Operators

by V.K. Dobrev

Symmetry 2022, 14(4), 660; https://doi.org/10.3390/sym14040660 - 24 Mar 2022

Cited by 1 | Viewed by 1291

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebra

G_{2 (2)}

. We use both the minimal and the maximal Heisenberg parabolic subalgebras. We give the main [...] Read more.

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebra

G_{2 (2)}

. We use both the minimal and the maximal Heisenberg parabolic subalgebras. We give the main multiplets of indecomposable elementary representations. This includes the explicit parametrization of the intertwining differential operators between the ERs. These are new results applicable in all cases when one would like to use

G_{2 (2)}

invariant differential operators. Full article

(This article belongs to the Special Issue Manifest and Hidden Symmetries in Field and String Theories)

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9 pages, 333 KiB

Open AccessArticle

Homotopy Coherent Representations

by Tim Porter and Jim Stasheff

Symmetry 2022, 14(3), 553; https://doi.org/10.3390/sym14030553 - 9 Mar 2022

Cited by 2 | Viewed by 1403

Abstract

Homotopy coherence has a considerable history, albeit also by other names. For this volume highlighting symmetries, the appropriate use is homotopy coherence of representations, at one time known as representations up to homotopy/homotopy coherent representations. We present a brief semi-historical survey, providing [...] Read more.

Homotopy coherence has a considerable history, albeit also by other names. For this volume highlighting symmetries, the appropriate use is homotopy coherence of representations, at one time known as representations up to homotopy/homotopy coherent representations. We present a brief semi-historical survey, providing some links that may not be common knowledge. Full article

(This article belongs to the Special Issue Manifest and Hidden Symmetries in Field and String Theories)

18 pages, 359 KiB

Open AccessFeature PaperArticle

Superspace BRST/BV Operators of Superfield Gauge Theories

by Ioseph Lvovich Buchbinder, Sylvester James Gates, Jr. and Konstantinos Koutrolikos

Symmetry 2022, 14(2), 256; https://doi.org/10.3390/sym14020256 - 28 Jan 2022

Cited by 1 | Viewed by 1544

Abstract

We consider the superspace BRST and BV description of

4 D, N = 1

super-Maxwell theory and its non-abelian generalization Super Yang–Mills. By fermionizing the superspace gauge transformation of the gauge superfields, we define the nilpotent superspace BRST symmetry transformation (

𝓈

[...] Read more.

We consider the superspace BRST and BV description of

4 D, N = 1

super-Maxwell theory and its non-abelian generalization Super Yang–Mills. By fermionizing the superspace gauge transformation of the gauge superfields, we define the nilpotent superspace BRST symmetry transformation (

𝓈

). After introducing an appropriate set of anti-superfields and defining the superspace antibracket, we use it to construct the BV-BRST nilpotent differential operator (

s

) in terms of superspace covariant derivatives. The anti-superfield independent terms of

s

provide a superspace generalization of the Koszul–Tate resolution (

δ

). In the linearized limit, the set of superspace differential operators that appear in

s

satisfy a nonlinear algebra which can be used to construct a BRST charge Q, without requiring pure spinor variables. Q acts on the Hilbert space of superfield states, and its cohomology generates the expected superspace equations of motion. Full article

(This article belongs to the Special Issue Manifest and Hidden Symmetries in Field and String Theories)

13 pages, 308 KiB

Open AccessArticle

Coadjoint Orbits of the Poincaré Group for Discrete-Spin Particles in Any Dimension

by Ismael Ahlouche Lahlali, Nicolas Boulanger and Andrea Campoleoni

Symmetry 2021, 13(9), 1749; https://doi.org/10.3390/sym13091749 - 19 Sep 2021

Cited by 5 | Viewed by 1534

Abstract

Considering the Poincaré group

I S O (d - 1, 1)

in any dimension

d > 3

, we characterise the coadjoint orbits that are associated with massive and massless particles of discrete spin. We also comment on how our [...] Read more.

Considering the Poincaré group

I S O (d - 1, 1)

in any dimension

d > 3

, we characterise the coadjoint orbits that are associated with massive and massless particles of discrete spin. We also comment on how our analysis extends to the case of continuous spin. Full article

(This article belongs to the Special Issue Manifest and Hidden Symmetries in Field and String Theories)

24 pages, 376 KiB

Open AccessArticle

Gauging the Higher-Spin-Like Symmetries by the Moyal Product. II

by Maro Cvitan, Predrag Dominis Prester, Stefano Gregorio Giaccari, Mateo Paulišić and Ivan Vuković

Symmetry 2021, 13(9), 1581; https://doi.org/10.3390/sym13091581 - 27 Aug 2021

Cited by 1 | Viewed by 1520

Abstract

Continuing the study of the Moyal Higher Spin Yang–Mills theory started in our previous paper we provide a detailed discussion of matter coupling and the corresponding tree-level amplitudes. We also start the investigation of the spectrum by expanding the master fields in terms [...] Read more.

Continuing the study of the Moyal Higher Spin Yang–Mills theory started in our previous paper we provide a detailed discussion of matter coupling and the corresponding tree-level amplitudes. We also start the investigation of the spectrum by expanding the master fields in terms of ordinary spacetime fields. We note that the spectrum can be consistent with unitarity while still preserving Lorentz covariance, albeit not in the usual way, but by employing an infinite-dimensional unitary representation of the Lorentz group. Full article

(This article belongs to the Special Issue Manifest and Hidden Symmetries in Field and String Theories)

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14 pages, 598 KiB

Open AccessArticle

Solutions of the Bullough–Dodd Model of Scalar Field through Jacobi-Type Equations

by Rodica Cimpoiasu, Radu Constantinescu and Alina Streche Pauna

Symmetry 2021, 13(8), 1529; https://doi.org/10.3390/sym13081529 - 19 Aug 2021

Cited by 1 | Viewed by 1601

Abstract

A technique based on multiple auxiliary equations is used to investigate the traveling wave solutions of the Bullough–Dodd (BD) model of the scalar field. We place the model in a flat and homogeneous space, considering a symmetry reduction to a 2D-nonlinear equation. It [...] Read more.

A technique based on multiple auxiliary equations is used to investigate the traveling wave solutions of the Bullough–Dodd (BD) model of the scalar field. We place the model in a flat and homogeneous space, considering a symmetry reduction to a 2D-nonlinear equation. It is solved through this refined version of the auxiliary equation technique, and multiparametric solutions are found. The key idea is that the general elliptic equation, considered here as an auxiliary equation, degenerates under some special conditions into subequations involving fewer parameters. Using these subequations, we successfully construct, in a unitary way, a series of solutions for the BD equation, part of them not yet reported. The technique of multiple auxiliary equations could be employed to handle several other types of nonlinear equations, from QFT and from various other scientific areas. Full article

(This article belongs to the Special Issue Manifest and Hidden Symmetries in Field and String Theories)

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40 pages, 507 KiB

Open AccessFeature PaperArticle

The σ₋ Cohomology Analysis for Symmetric Higher-Spin Fields

by Alexey S. Bychkov, Kirill A. Ushakov and Mikhail A. Vasiliev

Symmetry 2021, 13(8), 1498; https://doi.org/10.3390/sym13081498 - 16 Aug 2021

Cited by 5 | Viewed by 1780

Abstract

In this paper, we present a complete proof of the so-called First On-Shell Theorem that determines dynamical content of the unfolded equations for free symmetric massless fields of arbitrary integer spin in any dimension and arbitrary integer or half-integer spin in four dimensions. [...] Read more.

In this paper, we present a complete proof of the so-called First On-Shell Theorem that determines dynamical content of the unfolded equations for free symmetric massless fields of arbitrary integer spin in any dimension and arbitrary integer or half-integer spin in four dimensions. This is achieved by calculation of the respective

σ_{-}

cohomology both in the tensor language in Minkowski space of any dimension and in terms of spinors in

A d S_{4}

. In the d-dimensional case

H^{p} (σ_{-})

is computed for any p and interpretation of

H^{p} (σ_{-})

is given both for the original Fronsdal system and for the associated systems of higher form fields. Full article

(This article belongs to the Special Issue Manifest and Hidden Symmetries in Field and String Theories)

22 pages, 373 KiB

Open AccessArticle

Noether Currents and Maxwell-Type Equations of Motion in Higher Derivative Gravity Theories

by Taichiro Kugo

Symmetry 2021, 13(8), 1408; https://doi.org/10.3390/sym13081408 - 2 Aug 2021

Cited by 3 | Viewed by 1351

Abstract

In general coordinate invariant gravity theories whose Lagrangians contain arbitrarily high order derivative fields, the Noether currents for the global translation and for the Nakanishi’s

I O S p (8 | 8)

choral symmetry containing the BRS symmetry as its member [...] Read more.

In general coordinate invariant gravity theories whose Lagrangians contain arbitrarily high order derivative fields, the Noether currents for the global translation and for the Nakanishi’s

I O S p (8 | 8)

choral symmetry containing the BRS symmetry as its member are constructed. We generally show that for each of these Noether currents, a suitable linear combination of equations of motion can be brought into the form of a Maxwell-type field equation possessing the Noether current as its source term. Full article

(This article belongs to the Special Issue Manifest and Hidden Symmetries in Field and String Theories)

54 pages, 1793 KiB

Open AccessArticle

Circuit Complexity from Cosmological Islands

by Sayantan Choudhury, Satyaki Chowdhury, Nitin Gupta, Anurag Mishara, Sachin Panneer Selvam, Sudhakar Panda, Gabriel D. Pasquino, Chiranjeeb Singha and Abinash Swain

Symmetry 2021, 13(7), 1301; https://doi.org/10.3390/sym13071301 - 20 Jul 2021

Cited by 52 | Viewed by 3946

Abstract

Recently, in various theoretical works, path-breaking progress has been made in recovering the well-known page curve of an evaporating black hole with quantum extremal islands, proposed to solve the long-standing black hole information loss problem related to the unitarity issue. Motivated by this [...] Read more.

Recently, in various theoretical works, path-breaking progress has been made in recovering the well-known page curve of an evaporating black hole with quantum extremal islands, proposed to solve the long-standing black hole information loss problem related to the unitarity issue. Motivated by this concept, in this paper, we study cosmological circuit complexity in the presence (or absence) of quantum extremal islands in negative (or positive) cosmological constant with radiation in the background of Friedmann-Lema

\hat{i}

tre-Robertson-Walker (FLRW) space-time, i.e., the presence and absence of islands in anti de Sitter and the de Sitter space-time having SO(2, 3) and SO(1, 4) isometries, respectively. Without using any explicit details of any gravity model, we study the behavior of the circuit complexity function with respect to the dynamical cosmological solution for the scale factors for the above mentioned two situations in FLRW space-time using squeezed state formalism. By studying the cosmological circuit complexity, out-of-time ordered correlators, and entanglement entropy of the modes of the squeezed state, in different parameter space, we conclude the non-universality of these measures. Their remarkably different features in the different parameter space suggests their dependence on the parameters of the model under consideration. Full article

(This article belongs to the Special Issue Manifest and Hidden Symmetries in Field and String Theories)

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26 pages, 400 KiB

Open AccessArticle

Perturbative and Non-Pertrubative Trace Anomalies

by Loriano Bonora

Symmetry 2021, 13(7), 1292; https://doi.org/10.3390/sym13071292 - 18 Jul 2021

Cited by 3 | Viewed by 1489

Abstract

We study the definition of trace anomalies for models of Dirac and Weyl fermions coupled to a metric and a gauge potential. While in the non-perturbative case the trace anomaly is the response of the effective action to a Weyl transformation, the definition [...] Read more.

We study the definition of trace anomalies for models of Dirac and Weyl fermions coupled to a metric and a gauge potential. While in the non-perturbative case the trace anomaly is the response of the effective action to a Weyl transformation, the definition in a perturbative approach is more involved. In the latter case, we use a specific formula proposed by M.Duff, of which we present a physical interpretation. The main body of the paper consists in deriving trace anomalies with the above formula and comparing them with the corresponding non-perturbative results. We show that they coincide and stress the basic role of diffeomorphism invariance for the validity of the approach. Full article

(This article belongs to the Special Issue Manifest and Hidden Symmetries in Field and String Theories)

20 pages, 1334 KiB

Open AccessArticle

Wilsonian Effective Action and Entanglement Entropy

by Satoshi Iso, Takato Mori and Katsuta Sakai

Symmetry 2021, 13(7), 1221; https://doi.org/10.3390/sym13071221 - 7 Jul 2021

Cited by 11 | Viewed by 2352

Abstract

This is a continuation of our previous works on entanglement entropy (EE) in interacting field theories. In previous papers, we have proposed the notion of

Z_{M}

gauge theory on Feynman diagrams to calculate EE in quantum field theories and shown that EE [...] Read more.

This is a continuation of our previous works on entanglement entropy (EE) in interacting field theories. In previous papers, we have proposed the notion of

Z_{M}

gauge theory on Feynman diagrams to calculate EE in quantum field theories and shown that EE consists of two particular contributions from propagators and vertices. We have also shown that the purely non-Gaussian contributions from interaction vertices can be interpreted as renormalized correlation functions of composite operators. In this paper, we will first provide a unified matrix form of EE containing both contributions from propagators and (classical) vertices, and then extract further non-Gaussian contributions based on the framework of the Wilsonian renormalization group. It is conjectured that the EE in the infrared is given by a sum of all the vertex contributions in the Wilsonian effective action. Full article

(This article belongs to the Special Issue Manifest and Hidden Symmetries in Field and String Theories)

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15 pages, 319 KiB

Open AccessFeature PaperArticle

Properties of an Alternative Off-Shell Formulation of 4D Supergravity

by Friedemann Brandt

Symmetry 2021, 13(4), 620; https://doi.org/10.3390/sym13040620 - 8 Apr 2021

Cited by 1 | Viewed by 1185

Abstract

This article elaborates on an off-shell formulation of D = 4, N = 1 supergravity whose auxiliary fields comprise an antisymmetric tensor field without gauge degrees of freedom. In particular, the relation to new minimal supergravity, a supercovariant tensor calculus and the construction [...] Read more.

This article elaborates on an off-shell formulation of D = 4, N = 1 supergravity whose auxiliary fields comprise an antisymmetric tensor field without gauge degrees of freedom. In particular, the relation to new minimal supergravity, a supercovariant tensor calculus and the construction of invariant actions including matter fields are discussed. Full article

(This article belongs to the Special Issue Manifest and Hidden Symmetries in Field and String Theories)

4 pages, 467 KiB

Open AccessFeature PaperArticle

On the Trace Anomaly of the Chaudhuri–Choi–Rabinovici Model

by Yu Nakayama

Symmetry 2021, 13(2), 276; https://doi.org/10.3390/sym13020276 - 5 Feb 2021

Cited by 1 | Viewed by 1192

Abstract

Recently a non-supersymmetric conformal field theory with an exactly marginal deformation in the large N limit was constructed by Chaudhuri–Choi–Rabinovici. On a non-supersymmetric conformal manifold, the c coefficient of the trace anomaly in four dimensions would generically change. In this model, we, however, [...] Read more.

Recently a non-supersymmetric conformal field theory with an exactly marginal deformation in the large N limit was constructed by Chaudhuri–Choi–Rabinovici. On a non-supersymmetric conformal manifold, the c coefficient of the trace anomaly in four dimensions would generically change. In this model, we, however, find that it does not change in the first non-trivial order given by three-loop diagrams. Full article

(This article belongs to the Special Issue Manifest and Hidden Symmetries in Field and String Theories)

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