A-twisted Landau-Ginzburg models

TL;DR

This paper explores correlation functions in A-twisted Landau-Ginzburg models over complex spaces, providing new insights into their nontrivial geometric and quantum properties beyond traditional vector space cases.

Contribution

It presents the first detailed analysis of A-twisted Landau-Ginzburg models on nontrivial spaces, extending understanding beyond B-twisted models and vector space cases.

Findings

Computed correlation functions for models on nontrivial spaces

Provided tests of virtual fundamental class computations

Connected Landau-Ginzburg models to nonlinear sigma models on Calabi-Yaus

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.