Characters of admissible representations of the affine superalgebra sl(2|1)

TL;DR

This paper computes characters and supercharacters of admissible representations of the affine superalgebra sl(2|1), explores their modular properties, and links non-degenerate integrable characters to N=4 superconformal characters.

Contribution

It provides explicit character formulas for admissible representations of sl(2|1) and analyzes their modular behavior, connecting to superconformal theories.

Findings

Characters and supercharacters calculated for Ramond and Neveu-Schwarz sectors

Modular properties analyzed at level k=-1/2

Non-degenerate integrable characters match N=4 superconformal characters

Abstract

We calculate characters and supercharacters for irreducible, admissible representations of the affine superalgebra sl(2|1) in both the Ramond and Neveu-Schwarz sectors and discuss their modular properties in the special case of level k=-1/2. We also show that the non-degenerate integrable characters coincide with some N=4 superconformal characters.