Deformed quantum cohomology and (0,2) mirror symmetry

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 ${\mathbb{P}^1} \times {\mathbb{P}^1}$, 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. [1] and Katz and Sharpe [17]. We find immediate agreement with the latter and an interesting puzzle in completely matching the chiral ring of the former.