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

TL;DR

This work constructs a three-dimensional CS supergravity theory invariant under the $ ext{N}=1$ AdS Carroll superalgebra by applying the Concha contraction method to the $ ext{osp}(2|1) imes ext{sp}(2)$ AdS theory, yielding an action with two couplings $oldsymbol{ ilde{oldsymbol{ ilde{oldsymbol{ ilde{oldsymbol{ au}}}}}}$ and $oldsymbol{ ilde{oldsymbol{ ilde{oldsymbol{ ilde{oldsymbol{oldsymbol{ au}}}}}}}$ and explicit SUSY transformations. It then performs a flat limit $oldsymbol{ ilde{oldsymbol{ ilde{oldsymbol{ ilde{oldsymbol{ au}}}}}} o ext{Carroll}$, obtaining the $ ext{N}=1$ super-Carroll CS supergravity with a corresponding action, gauge structure, and field equations, and shows that the bosonic sector reproduces Carroll gravity. The results provide a concrete supersymmetric Carroll gravity model in $D=3$, enabling further exploration of holography, boundary dynamics, and asymptotic symmetries in ultra-relativistic contexts, and set the stage for extended ($ ext{N}>1$) Carroll CS supergravities. These constructions offer a controlled framework to study flat-space holography and potential boundary phenomena in ultra-relativistic gravity.

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.