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.
"Elliptic genera of Landau–Ginzburg models over nontrivial spaces." Adv. Theor. Math. Phys. 16 (4) 1087 - 1144, August 2012.