The supersymmetric sigma model and the geometry of the Weyl-Kac character formula

TL;DR

This paper constructs a supersymmetric field theory linking geometric and algebraic structures, explicitly computing the Weyl-Kac character formula via a steepest descent method.

Contribution

It introduces a novel supersymmetric field theory framework that connects the geometry of loop groups with the Weyl-Kac character formula, providing explicit computational techniques.

Findings

Explicit computation of the Weyl-Kac character formula

Connection between supersymmetric field theory and loop group representations

Application of steepest descent approximation to character formulas

Abstract

Field theoretic and geometric ideas are used to construct a chiral supersymmetric field theory whose ground state is a specified irreducible representation of a centrally extended loop group. The character index of the associated supercharge (an appropriate Dirac operator on $LG/T$) is the Weyl-K\v{a}c character formula which we compute explicitly by the steepest descent approximation.