Polytopes, supersymmetry, and integrable systems

TL;DR

This paper explores the mathematical connections between Lie-theoretic polytopes, integrable systems, and supersymmetry, providing a systematic framework that supports earlier physical theories linking these areas.

Contribution

It offers a new systematic mathematical treatment of the links between polytopes, integrable systems, and supersymmetry, clarifying the role of the Coxeter Plane in these connections.

Findings

Relation of Coxeter Plane to integrable systems clarified

Mathematical framework supporting physical theories established

Further insights into Lie-theoretic polytopes and field theories gained

Abstract

We review some links between Lie-theoretic polytopes and field theories in physics, which were proposed in the 1990's. A basic ingredient is the Coxeter Plane, whose relation to integrable systems and the Stokes Phenomenon has only recently come to light. We use this to give a systematic mathematical treatment, which gives further support to the physical proposals. This article is based on a talk which was scheduled to be given at the workshop "Representations of Discrete Groups and Geometric Topology on Manifolds", Josai University, 12-13 March 2020.