Enlarged super-$\mathfrak{bms}_{3}$ algebra and its flat limit

Abstract

In this paper we analyze the asymptotic symmetries of the three-dimensional Chern-Simons supergravity for a supersymmetric extension of the semi-simple enlargement of the Poincar\'e algebra, also known as AdS-Lorentz superalgebra, which is characterized by two fermionic generators. We propose a consistent set of asymptotic boundary conditions for the aforementioned supergravity theory, and we show that the corresponding charge algebra defines a supersymmetric extension of the semi-simple enlargement of the $\mathfrak{bms}_{3}$ algebra, with three independent central charges. This asymptotic symmetry algebra can alternatively be written as the direct sum of three copies of the Virasoro algebra, two of which are augmented by supersymmetry. Interestingly, we show that the flat limit of the obtained asymptotic algebra corresponds to a deformed super-$\mathfrak{bms}_{3}$ algebra, being the charge algebra of the minimal Maxwell supergravity theory in three dimensions.