Notes on certain other (0,2) correlation functions

TL;DR

This paper explores correlation functions in perturbative heterotic strings, generalizing B model computations to (0,2) theories, and discusses how classical properties extend and differ in quantum regimes, including a weakened Calabi-Yau condition.

Contribution

It provides a detailed analysis of (0,2) correlation functions, generalizing B model results and examining quantum effects and conditions like the Calabi-Yau property.

Findings

Correlation functions in heterotic strings generalize B model computations.

Quantum corrections differ between (0,2) A and B models.

Weakening the Calabi-Yau condition affects the (2,2) B model description.

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.