AdS Carroll Chern-Simons supergravity in 2 + 1 dimensions and its flat limit

Lucrezia Ravera

doi:10.1016/j.physletb.2019.06.026

Abstract

Carroll symmetries arise when the velocity of light is sent to zero (ultra-relativistic limit). In this paper, we present the construction of the three-dimensional Chern-Simons supergravity theory invariant under the so-called AdS Carroll superalgebra, which was obtained in the literature as a contraction of the AdS superalgebra. The action is characterized by two coupling constants. Subsequently, we study its flat limit, obtaining the three-dimensional Chern-Simons supergravity theory invariant under the super-Carroll algebra, which is a contraction of the Poincaré superalgebra. We apply the flat limit at the level of the superalgebra, Chern-Simons action, supersymmetry transformation laws, and field equations.

Highlights

Spacetime symmetries have played a fundamental role in the understanding of diverse physical theories such as Newtonian gravity, Maxwell’s electromagnetism, special and general relativity, string and supergravity theory
These non-relativistic gravity theories are all invariant under reparametrizations, but differ in the fact that they are invariant under distinct extensions of the Galilei symmetries, the latter arising when the velocity of light is sent to infinity (c → ∞, non-relativistic limit)
The simplest example is given by the so-called Galilei gravity theory, which is invariant under the unextended Galilei symmetries [2], while Newtonian gravity and its frame-independent reformulation, Newton-Cartan gravity, are invariant under the symmetries corresponding to a central extension of the Galilei algebra, called the Bargmann algebra [3,4,5]

Summary

Introduction

Spacetime symmetries have played a fundamental role in the understanding of diverse physical theories such as Newtonian gravity, Maxwell’s electromagnetism, special and general relativity, string and supergravity theory. In [41, 42] conformal extensions of the Carroll group were explored and related to the BMS group, and in [43,44,45,46] the authors shewed how Carrollian structures and geometry emerge in the framework of flat holography and fluid/gravity correspondence Motivated by all these interesting applications of Carroll symmetries and by the fact that a study of their supersymmetric extensions in the context of supergravity models is still lacking, in this work we present for the first time the construction of the three-dimensional CS supergravity theory invariant under the N = 1 AdS Carroll superalgebra (in D = 3, where here and in the sequel with D = 3 we mean 2 + 1 dimensions) introduced in [28] (which was obtained in [28] as a contraction of the N = 1 AdS superalgebra) by applying the method of [51].

Study of the flat limit

Final remarks