Smooth modules over the N=1 Bondi-Metzner-Sachs superalgebra

TL;DR

This paper develops a determinant formula for Verma modules over the N=1 BMS superalgebra, characterizes simple smooth modules, and constructs a free field realization to generate natural modules including Fock and Whittaker modules.

Contribution

It introduces a determinant formula for irreducibility, characterizes a new class of smooth modules, and constructs a free field realization for the N=1 BMS superalgebra.

Findings

Determinant formula for Verma modules established

Characterization of simple smooth modules achieved

Construction of free field realization and natural modules

Abstract

In this paper, we present a determinant formula for the contravariant form on Verma modules over the N=1 Bondi-Metzner-Sachs (BMS) superalgebra. This formula establishes a necessary and sufficient condition for the irreducibility of the Verma modules. We then introduce and characterize a class of simple smooth modules that generalize both Verma and Whittaker modules over the N=1 BMS superalgebra. We also utilize the Heisenberg-Clifford vertex superalgebra to construct a free field realization for the N=1 BMS superalgebra. This free field realization allows us to obtain a family of natural smooth modules over the N=1 BMS superalgebra, which includes Fock modules and certain Whittaker modules.