Fixed points of (0,2) Landau-Ginzburg renormalization group flows and the chiral algebra

TL;DR

This paper investigates (0,2) supersymmetric Landau-Ginzburg models in two dimensions, using chiral algebra constraints to analyze renormalization group flows and identify potential inconsistencies with unitarity in the IR superconformal theories.

Contribution

It introduces a method to use chiral algebra structures to constrain IR dynamics of (0,2) theories and highlights cases where these structures conflict with unitarity.

Findings

Chiral algebra incompatibility with unitarity in some IR theories

Constraints on IR superconformal field theories from chiral algebra analysis

Implications for classifying (0,2) SCFTs from Lagrangian flows

Abstract

We discuss renormalization group flows in two-dimensional quantum field theories with (0,2) supersymmetry. We focus on theories with UV described by a Landau-Ginzburg Lagrangian and use the chiral algebra to constrain the IR dynamics. We present examples where the structure of the chiral algebra is incompatible with unitarity of the IR superconformal theory and discuss the implications of this result for programs of classifying (0,2) SCFTs as endpoints of flows from simple Lagrangian theories.