Solitons in Two--Dimensional Topological Field Theories

TL;DR

This paper explores solitonic solutions in two-dimensional N=2 supersymmetric theories, demonstrating how they can be twisted into topological models with BRST symmetry and analyzing their quantization.

Contribution

It introduces a method to twist N=2 supersymmetric theories into topological sectors and studies solitons within these models, including explicit quantization examples.

Findings

Existence of classical solitons in the models.

Topological twisting leads to BRST-exact energy-momentum tensor.

Quantization of free and interacting models is achieved.

Abstract

We consider a class of $N=2$ supersymmetric non--unitary theories in two--dimensional Minkowski spacetime which admit classical solitonic solutions. We show how these models can be twisted into a topological sector whose energy--momentum tensor is a BRST commutator. There is an infinite number of degrees of freedom associated to the zero modes of the solitons. As explicit realizations of such models we discuss the BRST quantization of a system of free fields, while in the interacting case we study $N=2$ complexified twisted Toda theories.