Isomonodromy Aspects of the tt* Equations of Cecotti and Vafa I. Stokes Data

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 SLnR/SOn SLnR/SOn ) in terms of (1) asymptotic data, (2) holomorphic data, and (3) monodromy data, and we compute all of this data explicitly. This allows us, in particular, to find all solutions with integral Stokes data. These include solutions associated to non-linear sigma models (quantum cohomology) or Landau–Ginzburg models (unfoldings of singularities), as conjectured by Cecotti and Vafa in the 1990s.