Chiral algebras in Landau-Ginzburg models

TL;DR

This paper explores the structure of chiral algebras in two-dimensional supersymmetric Landau-Ginzburg models, demonstrating their invariance under renormalization group flow and analyzing their operator equations of motion.

Contribution

It provides a detailed analysis of chiral algebras in $ =(0,2)$ and $ =(2,2)$ Landau-Ginzburg models, highlighting their invariance and classical operator relations.

Findings

Chiral algebra is RG invariant in theories with R-symmetry.

Operator equations of motion determine the chiral algebra.

Classical form of operator equations is preserved quantum mechanically.

Abstract

Chiral algebras in the cohomology of the $\overline{Q}_+$ supercharge of two-dimensional $\mathcal{N}=(0,2)$ theories on flat spacetime are discussed. Using the supercurrent multiplet, we show that the answer is renormalization group invariant for theories with an R-symmetry. For $\mathcal{N}=(0,2)$ Landau-Ginzburg models, the chiral algebra is determined by the operator equations of motion, which preserve their classical form, and quantum renormalization of composite operators. We study these theories and then specialize to the $\mathcal{N}=(2,2)$ models and consider some examples.