Grassmannian Sigma Models and Topological-Antitopological Fusion

TL;DR

This paper analyzes topological-antitopological fusion equations for supersymmetric sigma models on Grassmannian manifolds, providing solutions for the metric and insights into vacua, solitons, and large N behavior.

Contribution

It introduces a diagonal basis simplifying the tt* equations for Grassmannian sigma models and relates their metrics to those of CP^{N-1} models, including large N solutions.

Findings

Diagonal basis simplifies tt* equations

Metric relates to CP^{N-1} models

Large N limit solutions are obtained

Abstract

We study the topological-antitopological fusion equations for supersymmetric sigma models on Grassmannian manifolds G(k,N). We find a basis in which the metric becomes diagonal and the $tt^*$ equations become tractable. The solution for the metric of G(k,N) can then be described in terms of the metric for the $CP^{N-1}$ models. The IR expansion helps clarify the picture of the vacua and gives the soliton numbers and masses. We also show that the $tt^*$ equation for G(k,N) in the large N limit is solvable, for any k.