The (0,2) Exactly Solvable Structure of Chiral Rings, Landau-Ginzburg Theories and Calabi-Yau Manifolds

TL;DR

This paper identifies an exactly solvable (0,2) conformal field theory related to Calabi-Yau sigma-models and Landau-Ginzburg theories, establishing a precise correspondence between these models through chiral ring structures and Yukawa couplings.

Contribution

It constructs and analyzes an exactly solvable (0,2) theory connecting heterotic string vacua, Landau-Ginzburg models, and Calabi-Yau manifolds, with explicit calculations of Yukawa couplings and chiral rings.

Findings

Complete agreement between Yukawa couplings and chiral ring product structures.

Derivation of the chiral ring's generating ideal from a (0,2) linear sigma-model.

Identification of the (0,2) exactly solvable theory as a fixed point of the conformal field theory.

Abstract

We identify the exactly solvable theory of the conformal fixed point of (0,2) Calabi-Yau sigma-models and their Landau-Ginzburg phases. To this end we consider a number of (0,2) models constructed from a particular (2,2) exactly solvable theory via the method of simple currents. In order to establish the relation between exactly solvable (0,2) vacua of the heterotic string, (0,2) Landau-Ginzburg orbifolds, and (0,2) Calabi-Yau manifolds, we compute the Yukawa couplings in the exactly solvable model and compare the results with the product structure of the chiral ring which we extract from the structure of the massless spectrum of the exact theory. We find complete agreement between the two up to a finite number of renormalizations. For a particularly simple example we furthermore derive the generating ideal of the chiral ring from a (0,2) linear sigma-model which has both a Landau-Ginzburg and a (0,2) Calabi-Yau phase.