Two-Dimensional Models With (0,2) Supersymmetry: Perturbative Aspects

TL;DR

This paper explores perturbative features of two-dimensional (0,2) supersymmetric sigma models, linking physical properties like the one-loop beta function to complex geometric structures such as chiral differential operators.

Contribution

It provides a physical interpretation of the mathematical theory of chiral differential operators within (0,2) sigma models, especially regarding the one-loop beta function.

Findings

Understanding of the one-loop beta function via holomorphic data

Connection between supersymmetric sigma models and chiral differential operators

Foundation for studying nonperturbative aspects in a companion paper

Abstract

Certain perturbative aspects of two-dimensional sigma models with (0,2) supersymmetry are investigated. The main goal is to understand in physical terms how the mathematical theory of ``chiral differential operators'' is related to sigma models. In the process, we obtain, for example, an understanding of the one-loop beta function in terms of holomorphic data. A companion paper will study nonperturbative behavior of these theories.