Solvable Models in Two-Dimensional N=2 Theories

TL;DR

This paper explores exactly solvable two-dimensional N=2 supersymmetric models, including sigma models and minimal models, by analyzing their topological-antitopological fusion equations, revealing detailed properties across the renormalization group flow.

Contribution

It introduces a method to solve specific N=2 models exactly in the large superfield limit using fusion equations, advancing understanding of their non-perturbative properties.

Findings

Exact solutions for CPN models and Grassmannian sigma models.

Determination of soliton spectra and coupling dependence.

Insights into the structure of perturbed N=2 minimal models.

Abstract

N=2 supersymmetric field theories in two dimensions have been extensively studied in the last few years. Many of their properties can be determined along the whole renormalization group flow, like their coupling dependence and soliton spectra. We discuss here several models which can be solved completely, when the number of superfields is taken to be large, by studying their topological-antitopological fusion equations. These models are the CPN model, sigma models on Grassmannian manifolds, and certain perturbed $N=2$ Minimal model.