Kuznetsov Categories for Gauged Linear Sigma Models
David Favero, Daniel Kaplan, Tyler L. Kelly
TL;DR
This work defines Kuznetsov and anti-Kuznetsov categories for gauged linear sigma models (GLSMs) via chambers in the GIT fan and establishes foundational equivalences with derived categories of complete intersections. It proves toric Orlov-type decompositions: for Z as a complete intersection of ample divisors in a smooth projective toric variety X, D^{b}(coh Z) splits into a Kuznetsov component plus an exceptional collection, with the dual orthogonal side captured by -K under hypersurface q-conditions. It then extends these ideas to anti-Kuznetsov categories and Fano-visitor phenomena: any complete intersection of r≥2 ample divisors in a Fano GIT quotient X is a Fano visitor, with its Fano host realized as an anti-Kuznetsov category of a GLSM. Overall, the paper unifies GLSM-derived, VGIT, and toric-geometric decompositions to generalize Orlov-type results and KKLL-style phenomena in a broad categorical framework.
Abstract
We define Kuznetsov and anti-Kuznetsov categories for gauged linear sigma models. We show that for complete intersections of ample divisors in smooth projective toric varieties, the Kuznetsov category is left orthogonal to an exceptional collection. We prove that any complete intersection of $r \ge 2$ ample divisors in a Fano GIT quotient is a Fano visitor and the derived category of its Fano host is equivalent to an anti-Kuznetsov category of a gauged linear sigma model.