A-twisted Landau-Ginzburg models

TL;DR

This work develops $A$-twisted Landau-Ginzburg models defined on nontrivial spaces and analyzes their correlation functions to test RG universality with nonlinear sigma models on Calabi–Yau targets. By introducing a quasi-homogeneous $U(1)$ isometry and an appropriate R-symmetry redefinition, the authors construct a Lorentz-invariant $A$-twist for LG theories and study both perturbative and nonperturbative sectors, including explicit examples like the quintic and the conifold small resolution. They demonstrate that LG correlators reproduce known $A$-model results and provide simple physical realizations of virtual fundamental class computations, with correlation-function calculations interpolating between Euler-class insertions and Mathai–Quillen/Thom-class formulations via scaling arguments. The paper also discusses LG models on stacks and hybrid GLSM phases, outlining how these frameworks yield insights into GW theory, GLSM phases, and potential connections to broader dualities and mirror constructions. Overall, the results extend the toolbox for topological twists, offer concrete tests of universality across GLSMs and NLSMs, and suggest new avenues for relating GW theory, virtual classes, and stack-based LG descriptions.

Abstract

In this paper we discuss correlation functions in certain A-twisted Landau-Ginzburg models. Although B-twisted Landau-Ginzburg models have been discussed extensively in the literature, virtually no work has been done on A-twisted theories. In particular, we study examples of Landau-Ginzburg models over topologically nontrivial spaces - not just vector spaces - away from large-radius limits, so that one expects nontrivial curve corrections. By studying examples of Landau-Ginzburg models in the same universality class as nonlinear sigma models on nontrivial Calabi-Yaus, we obtain nontrivial tests of our methods as well as a physical realization of some simple examples of virtual fundamental class computations.