Hori-mological projective duality
  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. 
J{\o}rgen Vold Rennemo and Ed Segal
math.AG hep-th