Curvature constraints in heterotic Landau-Ginzburg models

TL;DR

This paper analyzes heterotic Landau-Ginzburg models, demonstrating how supersymmetry constrains the superpotential's holomorphicity and relates nonholomorphic parameters to curvature, extending previous mathematical frameworks.

Contribution

It provides a detailed analysis of supersymmetry constraints in heterotic Landau-Ginzburg models, including nonholomorphic superpotentials, supporting and extending prior claims about these constraints.

Findings

Supersymmetry invariance up to total derivative.

Constraints relating superpotential parameters to curvature.

Extension to nonholomorphic superpotentials.

Abstract

In this paper, we study a class of heterotic Landau-Ginzburg models. We show that the action can be written as a sum of BRST-exact and non-exact terms. The non-exact terms involve the pullback of the complexified Kahler form to the worldsheet and terms arising from the superpotential, which is a Grassmann-odd holomorphic function of the superfields. We then demonstrate that the action is invariant on-shell under supersymmetry transformations up to a total derivative. Finally, we extend the analysis to the case in which the superpotential is not holomorphic. In this case, we find that supersymmetry imposes a constraint which relates the nonholomorphic parameters of the superpotential to the Hermitian curvature. Various special cases of this constraint have previously been used to establish properties of Mathai-Quillen form analogues which arise in the corresponding heterotic Landau-Ginzburg models. There, it was claimed that supersymmetry imposes those constraints. Our goal in this paper is to support that claim. The analysis for the nonholomorphic case also reveals a constraint imposed by supersymmetry that we did not anticipate from studies of Mathai-Quillen form analogues.