Isomonodromy aspects of the tt* equations of Cecotti and Vafa I. Stokes data

TL;DR

This paper characterizes all smooth solutions of the tt*-Toda equations using asymptotic, holomorphic, and monodromy data, including those with integral Stokes data linked to models in quantum cohomology and singularity theory.

Contribution

It provides a comprehensive description of solutions to the tt*-Toda equations in terms of monodromy and Stokes data, confirming conjectures related to models in physics and geometry.

Findings

Classifies solutions via monodromy data

Identifies solutions with integral Stokes data

Connects solutions to quantum cohomology and Landau-Ginzburg models

Abstract

We describe all smooth solutions of the two-function tt*-Toda equations (a version of the tt* equations, or equations for harmonic maps into SL(n,R)/SO(n)) in terms of (i) asymptotic data, (ii) holomorphic data, and (iii) monodromy data. This allows us to find all solutions with integral Stokes data. These include solutions associated to nonlinear sigma models (quantum cohomology) or Landau-Ginzburg models (unfoldings of singularities), as conjectured by Cecotti and Vafa.