Cohomological Reduction of Sigma Models

TL;DR

This paper explores the use of cohomological methods to simplify 2D supersymmetric sigma models, enabling explicit calculations of correlation functions through BRST operator-based reductions in superspace models.

Contribution

It introduces a cohomological reduction scheme for supersymmetric sigma models and demonstrates its application to various symmetric and coset superspaces.

Findings

Reduction simplifies the models, making correlation functions more accessible.

Explicit examples include symmetric superspaces and coset superspaces.

The method provides a systematic way to analyze supersymmetric quantum field theories.

Abstract

This article studies some features of quantum field theories with internal supersymmetry, focusing mainly on 2-dimensional non-linear sigma models which take values in a coset superspace. It is discussed how BRST operators from the target space supersymmetry algebra can be used to identify subsectors which are often simpler than the original model and may allow for an explicit computation of correlation functions. After an extensive discussion of the general reduction scheme, we present a number of interesting examples, including symmetric superspaces $G/G^{\mathbb{Z}_2}$ and coset superspaces of the form $G/G^{\mathbb{Z}_4}$.