Kuznetsov has conjectured that Pfaffian varieties should admit noncommutative crepant resolutions which satisfy his Homological Projective Duality. We prove half the cases of this conjecture by interpreting and proving a duality of nonabelian gauged linear sigma models proposed by Hori.
"Hori-mological projective duality." Duke Math. J. 168 (11) 2127 - 2205, 15 August 2019. https://doi.org/10.1215/00127094-2019-0014