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



Martin A. Guest (Department of Mathematics, Faculty of Science and Engineering, Waseda University, Shinjuku, Tokyo, Japan)

Takashi Otofuji (College of Engineering, Nihon University, Koriyama, Fukushima, Japan)


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