三维N扩展麦克斯韦超重力：Chern-Simons理论新视角

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"这篇论文是关于物理学中的N扩展麦克斯韦超重力理论，它将这一理论与三维Chern-Simons理论联系起来，并探讨了如何在没有宇宙学常数的情况下构建这种理论。作者Patrick Concha来自智利瓦尔帕莱索的Pontiﬁcia Universidad Católica de Valparaíso的物理研究所。该研究发表在《Physics Letters B》上，是一篇开放获取的文章。" 在物理学中，超重力理论是一种包含超对称性的引力理论，超对称性允许粒子之间的对偶性，即每种费米子（具有半整数自旋）对应着一种玻色子（具有整数自旋）。N扩展的麦克斯韦超重力理论指的是包含N种这样的对称变换的理论，这里的N可以是任意正整数。在本文中，研究者引入了一个新的理论框架，这个框架基于具有中心电荷的N扩展麦克斯韦超代数以及so(N)内部对称生成器。中心电荷是超代数的一个关键特征，它使得超对称生成元之间的代数关系更为复杂，同时也为理论提供了额外的自由度。so(N)内部对称性则意味着理论中存在N维旋转群的对称性，这允许构建一个非简并且不变的内积，这是定义理论的基础。有趣的是，新的N扩展超重力理论可以通过将N扩展的AdS-Lorentz超重力理论在某种限制下（平坦极限）扩展来得到，其中加入了so(N)规范场。AdS-Lorentz超重力理论是AdS（Anti-de Sitter）空间中的超重力理论，AdS空间是一种具有负曲率的时空间隔，常用于描述量子引力和弦理论的背景。在新理论中，由于特定的对称性和内积的存在，他们成功地构建了一个没有宇宙学常数项的超重力作用。宇宙学常数通常与暗能量相关，其非零值会导致宇宙加速膨胀。在这里，作者通过理论构造避免了这一常数，这可能为理解宇宙的动态提供新的视角。此外，Chern-Simons理论是一种拓扑量子场论，通常在低维空间中研究，它涉及到规范场与时空曲率的耦合。将N扩展的麦克斯韦超重力理论与Chern-Simons理论联系起来，暗示了理论的拓扑性质和可能的量子效应，这对于理解和探索量子引力的特性，特别是低维系统中的量子引力，具有重要意义。这篇论文的工作为超重力理论的研究开辟了新的途径，特别是通过与Chern-Simons理论的联系，可能对理解宇宙学、量子引力和对称性在物理学中的作用提供了新的洞察。开放获取的性质使得全球的研究人员都能访问和利用这些成果，促进科学知识的共享与进步。

Physics Letters B 792 (2019) 290–297

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

N -extended Maxwell supergravities as Chern-Simons theories in three

spacetime dimensions

Patrick Concha

Instituto de Física, Pontiﬁcia Universidad Católica de Valparaíso, Casilla 4059, Valparaiso-Chile

a r t i c l e i n f o a b s t r a c t

Article history:

Received

15 March 2019

Received

in revised form 26 March 2019

Accepted

28 March 2019

Available

online 2 April 2019

Editor:

M. Cveti

We present a new class of three-dimensional N -extended supergravity theories based on the N -extended

Maxwell superalgebra with central charges and so(N ) internal symmetry generators. The presence

of so(N ) generators is required in order to deﬁne a non-degenerate invariant inner product. Such

symmetry allows us to construct an alternative supergravity action without cosmological constant term.

Interestingly, the new theories can be obtained as a ﬂat limit of a N -extended AdS-Lorentz supergravity

theories enlarged with so(N ) gauge ﬁelds.

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

1. Introduction

It is well assumed that a three-dimensional (super)gravity the-

ory

can be described by a Chern-Simons (CS) action as a gauge

theory offering us an interesting toy model to approach higher-

dimensional

theories [1–11]. There has been a growing interest to

go beyond Poincaré and AdS (super)groups to describe (super)grav-

ity

theories in order to study new models with different physical

content [12–26]. In a previous work [27], we presented a new class

of three-dimensional supergravity theories based on the Maxwell

and AdS-Lorentz superalgebras.

the bosonic level, the Maxwell symmetry has been initially

introduced in [28–30]in order to describe a Minkowski space in

presence of a constant classical electromagnetic ﬁeld background.

Its generalization has been useful to recover General Relativity

from CS and Born-Infeld (BI) gravity actions [31–33]. Recently,

there has been a particular interest in exploring CS gravity model

invariant under the Maxwell algebra [34–37]. In particular, the

presence of the additional gauge ﬁeld inﬂuences the vacuum en-

ergy

and the vacuum angular momentum of the stationary conﬁg-

uration

[37].

the other hand, the AdS-Lorentz symmetry was ﬁrst intro-

duced

in [13,38] and can be seen as a semi-simple enlargement of

the Poincaré symmetry. Recently, the AdS-Lorentz algebra and its

generalizations have been used to recover diverse (pure)Lovelock

Lagrangian from CS and BI ones [39–41]. More recently, it has been

showed that the asymptotic symmetry of a three-dimensional CS

gravity action invariant under the AdS-Lorentz group is given by a

E-mail address: patrick.concha@pucv.cl.

semi-simple enlargement of the bms

symmetry which is isomor-

phic

to three copies of the Virasoro algebra [25].

the supersymmetric level, the Maxwell superalgebra has

been introduced to describe the presence of a constant abelian

supersymmetric gauge ﬁeld background in a four-dimensional su-

perspace

[42]. Interestingly, a pure supergravity action in four di-

mensions

can be constructed based on the Maxwell superalgebra

using a geometric procedure [43,44]. Recently it has been shown

in [45] that the bosonic extra ﬁeld and the additional Majorana

gauge ﬁeld, appearing in the Maxwell superalgebra, are crucial to

recover supersymmetry invariance of ﬂat supergravity on a man-

ifold

with non-trivial boundary. Extensions and generalizations of

the supersymmetric version of the Maxwell symmetries have been

extensively studied by diverse authors [46–56].

this paper we extend the results of [27] and present a new

class of N -extended CS supergravity theories in three spacetime

dimensions based on the central N -extended Maxwell superalge-

bra.

We show that the Maxwell superalgebra has to be enlarged

with so

(

)

generators in order to have non-degenerate invariant

inner product. Interestingly, the Maxwell superalgebra allows us to

deﬁne an alternative supergravity model in absence of cosmolog-

ical

constant term. The introduction of the cosmological constant

term is done by considering an enlarged superalgebra which cor-

responds

to a N -extended AdS-Lorentz superalgebra. In order to

establish a well-deﬁned Maxwell limit we extend the superalgebra

with so

(

)

internal symmetry algebra.

This

work is organized as follows: In Section 2, we give a brief

review of the three-dimensional minimal Maxwell CS supergravity

theory. The section 3 is devoted to the construction of the CS su-

pergravity

action invariant under the N = 2Maxwell superalgebra.

In section 4, we present a new class of N -extended supergrav-

https://doi.org/10.1016/j.physletb.2019.03.060

0370-2693/

SCOAP

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