Derived Kn"orrer periodicity and Orlov's theorem for gauged Landau-Ginzburg models

TL;DR

This paper establishes a Knörrer periodicity equivalence for gauged Landau-Ginzburg models, extending Orlov's theorem to relate categories of matrix factorizations and derived categories of hypersurfaces.

Contribution

It introduces a gauged LG version of Knörrer periodicity and applies it to derive a gauged LG analogue of Orlov's theorem, connecting different categorical frameworks.

Findings

Proved a Knörrer periodicity equivalence for gauged LG models.

Derived a gauged LG version of Orlov's theorem.

Connected categories of matrix factorizations with derived hypersurface categories.

Abstract

We prove a Kn"orrer periodicity type equivalence between derived factorization categories of gauged LG models, which is an analogy of a theorem proved by Shipman and Isik independently. As an application, we obtain a gauged LG version of Orlov's theorem describing a relationship between categories of graded matrix factorizations and derived categories of hypersurfaces in projective spaces, by combining the above Kn"orrer periodicity type equivalence and the theory of variations of GIT quotients due to Ballard, Favero and Katzarkov.