Topological-antitopological fusion and the quantum cohomology of Grassmannians

TL;DR

This paper explains the connection between the quantum cohomology of Grassmannians and projective spaces using tt* equations, linking physics, Lie theory, and geometric correspondences.

Contribution

It provides a Lie-theoretic interpretation of the Satake correspondence and relates tt* equations to quantum cohomology and integrable models.

Findings

Link between quantum cohomology of Grassmannians and projective spaces.

Lie-theoretic interpretation of the Satake correspondence.

Connection between particles in affine Toda models and sigma-model solitons.

Abstract

We suggest an explanation for the part of the Satake Correspondence which relates the quantum cohomology of complex Grassmannians and the quantum cohomology of complex projective space, as well as their respective Stokes data, based on the original physics approach using the tt* equations. We also use the Stokes data of the tt* equations to provide a Lie-theoretic link between particles in affine Toda models and solitons in certain sigma-models. Along the way, we illustrate some (well known) relations between the tt* equations, the non-abelian Hodge Correspondence, and quantum cohomology.