R-symmetries and curvature constraints in A-twisted heterotic Landau-Ginzburg models

TL;DR

This paper analyzes R-symmetries and curvature constraints in A-twisted heterotic Landau-Ginzburg models on Kähler varieties, focusing on anomaly-free examples and deformations of Mathai-Quillen forms related to supersymmetry.

Contribution

It classifies R-symmetries allowing A-twists in heterotic Landau-Ginzburg models with specific gauge bundle deformations and explores curvature constraints and Mathai-Quillen form deformations.

Findings

Identified anomaly-free R-symmetries for A-twisted models.

Reviewed curvature constraints from supersymmetry with non-holomorphic superpotentials.

Discussed deformations of Mathai-Quillen forms in the context of these models.

Abstract

In this paper, we discuss various aspects of a class of A-twisted heterotic Landau-Ginzburg models on a Kaehler variety X. We provide a classification of the R-symmetries in these models which allow the A-twist to be implemented, focusing on the case in which the gauge bundle is either a deformation of the tangent bundle of X or a deformation of a sub-bundle of the tangent bundle of X. Some anomaly-free examples are provided. The curvature constraint imposed by supersymmetry in these models when the superpotential is not holomorphic is reviewed. Constraints of this nature have been used to establish properties of analogues of pullbacks of Mathai-Quillen forms which arise in the correlation functions of the corresponding A-twisted or B-twisted heterotic Landau-Ginzburg models. The analogue most relevant to this paper is a deformation of the pullback of a Mathai-Quillen form. We discuss how this deformation may arise in the class of models studied in this paper. We then comment on how analogues of pullbacks of Mathai-Quillen forms not discussed in previous work may be obtained. Standard Mathai-Quillen formalism is reviewed in an appendix. We also include an appendix which discusses the deformation of the pullback of a Mathai-Quillen form.