Disordered $\mathcal{N} = (2, 2)$ Supersymmetric Field Theories

TL;DR

This paper studies disordered two-dimensional $ ext{N}=(2,2)$ supersymmetric theories, analyzing their correlation functions, conformal properties, and chaos behavior, revealing a rich structure with conformal manifolds and connections to Calabi-Yau models.

Contribution

It introduces and analyzes a class of disordered $ ext{N}=(2,2)$ supersymmetric models, including their correlation functions, conformal manifolds, and chaos exponents, extending previous Landau-Ginzburg and gauged linear sigma models.

Findings

Some models have a conformal manifold with variable chaos exponent.

The chaos exponent varies nontrivially along the conformal manifold.

Disordered gauged linear sigma models relate to ensemble averages of Calabi-Yau sigma models.

Abstract

We investigate a large class of $\mathcal{N} = (2, 2)$ supersymmetric field theories in two dimensions, which contains the Murugan-Stanford-Witten model, and can be naturally regarded as a disordered generalization of the two-dimensional Landau-Ginzburg models. We analyze the two and four-point functions of chiral superfields, and extract from them the central charge, the operator spectrum, and the chaos exponent in these models. Some of the models exhibit a conformal manifold parameterized by the variances of the random couplings. We compute the Zamolodchikov metrics on the conformal manifold, and demonstrate that the chaos exponent varies nontrivally along the conformal manifolds. Finally, we introduce and perform some preliminary analysis of a disordered generalization of the gauged linear sigma models, and discuss the low energy theories as ensemble averages of Calabi-Yau sigma models over complex structure moduli space.