三维Maxwell超重力理论与平坦极限研究

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"这篇研究论文发表在Physics Letters B 785 (2018) 247–253上，探讨了2+1维空间中的Maxwell超重力理论及其平坦极限。作者包括Patrick Concha, Diego M. Peñaﬁela和Evelyn Rodríguez，分别来自智利瓦尔帕莱索的Pontiﬁcia Universidad Católica de Valparaíso和Viña del Mar的Universidad Adolfo Ibáñez。该研究在2018年7月4日提交，8月23日修订，8月27日接受，并于8月30日在线发布，由M. Cvetiˇc担任编辑。" 文章的核心内容是关于三维Chern-Simons超重力理论的构建，这是在最小的Maxwell超代数框架下完成的。Chern-Simons理论是一种特殊类型的量子场论，它基于拓扑性质，通常用于描述引力和其他规范场的交互。在这个研究中，作者成功地构建了一个不受三个耦合常数影响的宇宙学常数项的超重力作用。宇宙学常数是描述宇宙膨胀速度的关键参数，其值的零表示平坦宇宙。 Maxwell超重力，正如文中所展示的，可以视为最小AdS（Anti-de Sitter）-洛伦兹超重力中宇宙常数趋于零的极限情况。AdS空间是一种负曲率的时空，与洛伦兹空间（我们日常体验的平坦空间时间）相对应。这一发现可能对理解不同宇宙模型和引力理论的相互关系有重要意义。平坦极限的分析不仅局限于超代数层面，还包括Chern-Simons动作和超对称变换的水平。Chern-Simons动作是超对称理论中的关键组成部分，它确保了理论的规范不变性。超对称变换则是粒子物理学和弦理论中的一种基本对称性，将玻色子与费米子联系起来。这项研究提供了对Maxwell超重力理论的深入理解，特别是在2+1维空间中的表现，以及它如何与其他超重力理论，如AdS-Lorentz超重力，相联系。这为探索高维物理、量子引力和宇宙学的理论框架提供了新的视角和工具。

Physics Letters B 785 (2018) 247–253

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

On the Maxwell supergravity and ﬂat limit in 2 + 1dimensions

Patrick Concha

a,∗

, Diego M. Peñaﬁel

, Evelyn Rodríguez

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

Departamento de Ciencias, Facultad de Artes Liberales, Universidad Adolfo Ibáñez, Viña del Mar, Chile

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

Article history:

Received

4 July 2018

Received

in revised form 23 August 2018

Accepted

27 August 2018

Available

online 30 August 2018

Editor: M.

Cveti

The construction of the three-dimensional Chern–Simons supergravity theory invariant under the

minimal Maxwell superalgebra is presented. We obtain a supergravity action without cosmological

constant term characterized by three coupling constants. We also show that the Maxwell supergravity

presented here appears as a vanishing cosmological constant limit of a minimal AdS–Lorentz supergravity.

The ﬂat limit is applied at the level of the superalgebra, Chern–Simons action, supersymmetry

transformation laws and ﬁeld equations.

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

1. Introduction

The three-dimensional (super)gravity is considered as an in-

teresting

toy model for approaching richer (super)gravity models,

which in general are non-trivial. Furthermore, the three-dimen-

sional

theory shares many interesting properties with higher-

dimensional

theories such as black hole solutions [1]. Remarkably,

supergravity theory in three spacetime dimensions [2,3]can be ex-

pressed

as a gauge theory using the Chern–Simons (CS) formalism

for the AdS [4]or Poincaré supergroup [5]. In the last decades, di-

verse

three-dimensional supergravity models have been studied in

[6–24]. In particular, there has been a growing interest to extend

AdS and Poincaré supergravity theories to other symmetries.

The

Maxwell symmetry has become an interesting alternative

for generalizing Einstein gravity. The Maxwell algebra has been in-

troduced

to describe a particle moving in a four-dimensional back-

ground

in the presence of a constant electromagnetic ﬁeld [25–27].

Further applications of the Maxwell group have been developed in

[28–30]. The Maxwell symmetry and its generalizations have been

useful to recover General Relativity (GR) as a particular limit us-

ing

the CS and Born–Infeld (BI) gravity formalism [31–35]. In four

dimensions, Maxwell gravity models have been successfully con-

structed

in [36–38]. More recently, there has been a growing inter-

est

in studying the three-dimensional CS gravity theory invariant

under the Maxwell group [39–43]. This theory, as the Poincaré one,

is asymptotically ﬂat and does not contain a cosmological constant

term. Interestingly, anovel asymptotic structure appears for the

Corresponding author.

E-mail

addresses: patrick.concha@pucv.cl (P. Concha), diego.molina.p@pucv.cl

(D.M. Peñaﬁel),

evelyn.rodriguez@edu.uai.cl (E. Rodríguez).

three-dimensional Maxwell CS gravity [43]. Such asymptotic sym-

metry

corresponds to a deformed bms

algebra and has been ﬁrst

introduced in [44]by using the semigroup expansion procedure

[45]. Furthermore, it has been shown that the vacuum energy and

angular momentum are inﬂuenced by the presence of the gravita-

tional

Maxwell ﬁeld [43].

The

Maxwell algebra also appears as an Inönü–Wigner (IW)

contraction [46,47]of an enlarged algebra known as AdS–Lorentz

algebra. The AdS–Lorentz algebra, also known as the semisim-

ple

extended Poincaré algebra, was introduced in [48,49] and has

been studied in the context of gravity in diverse dimensions [40,

50,51].

Such symmetry can be written as the semidirect sum

s0(d − 1, 2) ⊕ s0(d − 1, 1) which motivates the name of AdS–

Lorentz.

the supersymmetric level, a minimal extension of the

Maxwell algebra appears to describe the geometry of a four-

dimensional

superspace in presence of a constant abelian super-

symmetric

gauge ﬁeld background [52]. Subsequently in [53,54],

the Maxwell superalgebra has been used to construct a pure su-

pergravity

action in four dimensions using geometric methods.

Further applications of the Maxwell superalgebra in the context

of supergravity can be found in [55,56]. Such superalgebra has the

particularity of having more than one spinor charge and has been

obtained in [57,58]through algebraic expansion mechanisms [45,

59].

More recently, aCS gravity action for a generalized Maxwell

superalgebra has been presented in [60,61]in three spacetime di-

mensions.

Although the CS supergravity theory is appropriately

constructed, it requires to consider a large amount of gauge ﬁelds

whose origin is due to the methodology. To our knowledge, the

construction of a CS supergravity action for the minimal Maxwell

superalgebra in absence of extra ﬁelds has not been presented yet.

https://doi.org/10.1016/j.physletb.2018.08.050

0370-2693/

SCOAP

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