Elliptic genera of Landau-Ginzburg models over nontrivial spaces

TL;DR

This paper computes elliptic genera for supersymmetric Landau-Ginzburg models over complex nontrivial spaces, confirming their equivalence with nonlinear sigma models through explicit Thom class calculations.

Contribution

It extends elliptic genus computations to Landau-Ginzburg models on nontrivial spaces, generalizing previous results over vector spaces and orbifolds.

Findings

Elliptic genera match between Landau-Ginzburg and nonlinear sigma models.

Explicit Thom class computation confirms the equivalence.

Generalization to nontrivial spaces broadens applicability of elliptic genus calculations.

Abstract

In this paper, we discuss elliptic genera of (2,2) and (0,2) supersymmetric Landau-Ginzburg models over nontrivial spaces, i.e., nonlinear sigma models on nontrivial noncompact manifolds with superpotential, generalizing old computations in Landau-Ginzburg models over (orbifolds of) vector spaces. For Landau-Ginzburg models in the same universality class as nonlinear sigma models, we explicitly check that the elliptic genera of the Landau-Ginzburg models match that of the nonlinear sigma models, via a Thom class computation of a form analogous to that appearing in recent studies of other properties of Landau-Ginzburg models on nontrivial spaces.