Deformed Quantum Cohomology and (0,2) Mirror Symmetry

TL;DR

This paper computes instanton corrections in a (0,2) supersymmetric model with target space P1xP1, revealing deformed quantum cohomology and exploring mirror symmetry, with results matching some prior computations but presenting unresolved puzzles.

Contribution

It introduces a method to compute instanton corrections in (0,2) models and analyzes the resulting deformed chiral ring, advancing understanding of (0,2) mirror symmetry.

Findings

Agreement with Katz and Sharpe's results

Discrepancy with Adams et al.'s computations

Identification of a puzzle in matching chiral rings

Abstract

We compute instanton corrections to correlators in the genus-zero topological subsector of a (0,2) supersymmetric gauged linear sigma model with target space P1xP1, whose left-moving fermions couple to a deformation of the tangent bundle. We then deduce the theory's chiral ring from these correlators, which reduces in the limit of zero deformation to the (2,2) ring. Finally, we compare our results with the computations carried out by Adams et al.[ABS04] and Katz and Sharpe[KS06]. We find immediate agreement with the latter and an interesting puzzle in completely matching the chiral ring of the former.