Positive energy representations of affine algebras and Stokes matrices of the affine Toda equations

TL;DR

This paper constructs positive energy representations of affine Lie algebras using Stokes data from solutions to affine Toda equations, linking integrable systems with conformal field theory.

Contribution

It introduces a novel method to derive affine Lie algebra representations from Stokes data of affine Toda equations, with applications in conformal field theory.

Findings

Constructed positive energy representations from Stokes data.

Connected affine Toda solutions to conformal field theory models.

Illustrated with examples like fusion rings and W-algebra models.

Abstract

We give a construction which produces a positive energy representation of the affine Lie algebra of type A_n from the Stokes data of a solution of the tt*-Toda equations of type A_n. The construction appears to play a role in conformal field theory. We illustrate this with several examples: the fusion ring, W-algebra minimal models (Argyres-Douglas theory), as well as topological-antitopological fusion itself. (Minor typographical changes for this version.)