Smooth Modules of the 2D Supersymmetric Galilean Conformal Algebra

Abstract

The Galilean conformal algebra, a non-semisimple Lie algebra, is closely associated with the non-relativistic limit of the AdS/CFT correspondence. This paper investigates an infinite-dimensional Lie superalgebra called the 2D supersymmetric Galilean conformal algebra, which is obtained by the method of group contraction on 2D N = (2, 2) superconformal algebra. Physically, this superalgebra is relevant to superstring theory and the tricritical Ising model. We first construct a class of simple smooth modules induced from simple modules over finite-dimensional solvable Lie superalgebras. Furthermore, we provide several equivalent descriptions for simple smooth modules over the 2D supersymmetric Galilean conformal algebra. Additionally, examples of simple smooth modules such as the highest weight modules, Whittaker modules and high order Whittaker modules are presented.

Keywords

2D supersymmetric Galilean conformal algebra / smooth module / simple module

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