Notes on certain other (0,2) correlation functions

TL;DR

This work extends the $(0,2)$ analogue framework of the A-model to the B-model in perturbative heterotic strings, showing that quantum corrections can arise off the $(2,2)$ locus and depend sensitively on how induced sheaves are extended over compactified moduli spaces. It clarifies the A/B relation as more subtle than a simple dualization of the gauge bundle, identifying two regularization pathways that can yield distinct results and resolving apparent contradictions. The paper further demonstrates that the closed-string B-model can be defined on spaces with $K_X^{\otimes 2} \cong \mathcal{O}_X$, broadening the usual Calabi–Yau constraint, and provides explicit examples where quantum corrections vanish due to cohomological exactness, illustrating potential nonrenormalization phenomena. Together, these results connect GLSM regularization, sheaf-theoretic descriptions of instanton sectors, and potential auxiliary-field interpretations to deepen our understanding of $(0,2)$ quantum cohomology and mirror-like structures in heterotic settings.

Abstract

In this paper we shall describe some correlation function computations in perturbative heterotic strings that generalize B model computations. On the (2,2) locus, correlation functions in the B model receive no quantum corrections, but off the (2,2) locus, that can change. Classically, the (0,2) analogue of the B model is equivalent to the previously-discussed (0,2) analogue of the A model, but with the gauge bundle dualized -- our generalization of the A model, also simultaneously generalizes the B model. The A and B analogues sometimes have different regularizations, however, which distinguish them quantum-mechanically. We discuss how properties of the (2,2) B model, such as the lack of quantum corrections, are realized in (0,2) A model language. In an appendix, we also extensively discuss how the Calabi-Yau condition for the closed string B model (uncoupled to topological gravity) can be weakened slightly, a detail which does not seem to have been covered in the literature previously. That weakening also manifests in the description of the (2,2) B model as a (0,2) A model.