The Maxwell group in 2+1 dimensions and its infinite-dimensional enhancements

Self Cite

117

We construct finite-and infinite-dimensional non-relativistic extensions of the Newton-Hooke and Carroll (A)dS algebras using the algebra expansion method, starting from the (anti-)de Sitter relativistic algebra in D dimensions. These algebras are also shown to be embedded in different affine Kac-Moody algebras. In the three-dimensional case, we construct Chern-Simons actions invariant under these symmetries. This leads to a sequence of non-relativistic gravity theories, where the simplest examples correspond to extended Newton-Hooke and extended (post-)Newtonian gravity together with their Carrollian counterparts.

Section: A1 Non-relativistic Expansions Of the Maxwell Algebramentioning

confidence: 99%

Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity

Gomis

Kleinschmidt

Palmkvist

et al. 2020

Self Cite

117

“…Further application of the Maxwell algebra can be found in [49][50][51][52][53][54][55]. At the supersymmetric level, the minimal Maxwell superalgebra appears to describe a constant Abelian supersymmetric gauge field background in a four-dimensional superspace [56].…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional Maxwellian extended Bargmann supergravity

Concha

Ravera

Rodríguez

2020

We present a novel three-dimensional non-relativistic Chern-Simons supergravity theory invariant under a Maxwellian extended Bargmann superalgebra. We first study the nonrelativistic limits of the minimal and the N = 2 Maxwell superalgebras. We show that a well-defined Maxwellian extended Bargmann supergravity requires to construct by hand a supersymmetric extension of the Maxwellian extended Bargmann algebra by introducing additional fermionic and bosonic generators. The new non-relativistic supergravity action presented here contains the extended Bargmann supergravity as a sub-case.

“…The gauge field related to the new generator M µν modifies not only the asymptotic sector but also the vacuum energy and the vacuum angular momentum of the stationary configuration. More recently, an infinite-dimensional enhancement of the Maxwell group in 2+1 dimensions has been constructed in [79]. Generalizations and applications of the Maxwell symmetry can be found in the context of (super)gravity [80][81][82][83][84][85][86][87][88], higher-spin [89], non-relativistic models [90][91][92][93][94] among others.…”

Section: Introduction and Motivationsmentioning

confidence: 99%

On stabilization of Maxwell-BMS algebra

Concha

Safari

2020

In this work we present different infinite dimensional algebras which appear as deformations of the asymptotic symmetry of the three-dimensional Chern-Simons gravity for the Maxwell algebra. We study rigidity and stability of the infinite dimensional enhancement of the Maxwell algebra. In particular, we show that three copies of the Witt algebra and the bms 3 ⊕ witt algebra are obtained by deforming its ideal part. New family of infinite dimensional algebras are obtained by considering deformations of the other commutators which we have denoted as M(a, b; c, d) and M(ᾱ,β;ν). Interestingly, for the specific values a = c = d = 0, b = − 1 2 the obtained algebra M(0, − 1 2 ; 0, 0) corresponds to the twisted Schrödinger-Virasoro algebra. The central extensions of our results are also explored. The physical implications and relevance of the deformed algebras introduced here are discussed along the work.