Derived Knörrer periodicity and Orlov’s theorem for gauged Landau–Ginzburg models

Abstract

We prove a Knörrer-periodicity-type equivalence between derived factorization categories of gauged Landau–Ginzburg models, which is an analogy of a theorem proved by Shipman and Isik independently. As an application, we obtain a gauged Landau–Ginzburg 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 Knörrer periodicity type equivalence and the theory of variations of geometric invariant theory quotients due to Ballard, Favero and Katzarkov.