Hori-mological projective duality

TL;DR

This paper proves part of Kuznetsov's conjecture on non-commutative resolutions of Pfaffian varieties by establishing a duality in non-abelian gauged linear sigma models, advancing understanding of homological projective duality.

Contribution

It confirms half of Kuznetsov's conjecture by connecting non-commutative resolutions with Hori's duality in gauged linear sigma models.

Findings

Proves a duality of non-abelian gauged linear sigma models.

Supports Kuznetsov's conjecture on Pfaffian varieties.

Advances the theory of homological projective duality.

Abstract

Kuznetsov has conjectured that Pfaffian varieties should admit non-commutative crepant resolutions which satisfy his Homological Projective Duality. We prove half the cases of this conjecture, by interpreting and proving a duality of non-abelian gauged linear sigma models proposed by Hori.