(0,2) Landau-Ginzburg Models and Residues

TL;DR

This paper explores the structure of topological rings in (0,2) Landau-Ginzburg models, linking algebraic cohomology to physical correlators and generalizing residues, with applications to heterotic string compactifications.

Contribution

It introduces a novel framework connecting Koszul cohomology with topological correlators in (0,2) models, extending residue concepts beyond (2,2) theories.

Findings

Identifies the topological heterotic ring with Koszul cohomology groups.

Defines a generalized residue map for genus zero correlators.

Provides a method for computing Yukawa couplings in heterotic models.

Abstract

We study the topological heterotic ring in (0,2) Landau-Ginzburg models without a (2,2) locus. The ring elements correspond to elements of the Koszul cohomology groups associated to a zero-dimensional ideal in a polynomial ring, and the computation of half-twisted genus zero correlators reduces to a map from the first non-trivial Koszul cohomology group to complex numbers. This map is a generalization of the local Grothendieck residue. The results may be applied to computations of Yukawa couplings in a heterotic compactification at a Landau-Ginzburg point.