Equivalences between GIT quotients of Landau-Ginzburg B-models

TL;DR

This paper establishes a framework for B-branes in Landau-Ginzburg models, demonstrating quasi-equivalences between categories arising from different GIT quotients, and linking these to spherical twists.

Contribution

It generalizes the category of B-branes to non-affine Landau-Ginzburg models and proves quasi-equivalence between categories from different GIT quotients.

Findings

Categories of B-branes are quasi-equivalent for different GIT quotients.

Set of quasi-equivalences indexed by integers.

Auto-equivalences are spherical twists.

Abstract

We define the category of B-branes in a (not necessarily affine) Landau-Ginzburg B-model, incorporating the notion of R-charge. Our definition is a direct generalization of the category of perfect complexes. We then consider pairs of Landau-Ginzburg B-models that arise as different GIT quotients of a vector space by a one-dimensional torus, and show that for each such pair the two categories of B-branes are quasi-equivalent. In fact we produce a whole set of quasi-equivalences indexed by the integers, and show that the resulting auto-equivalences are all spherical twists.