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# Advances in Theoretical and Mathematical Physics

## Volume 26 (2022)

### Number 7

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

Pages: 2077 – 2093

DOI: https://dx.doi.org/10.4310/ATMP.2022.v26.n7.a3

#### Authors

#### Abstract

We give a construction which produces a positive energy representation of the affine Lie algebra $\widehat{\mathfrak{sl}}_{n+1} \mathbb{C}$ from the Stokes data of a solution of the $\mathrm{tt}^\ast$-Toda equations. 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.

Published 30 August 2023