Chiral Koszul duality

Original · EN

We extend the theory of chiral and factorization algebras, developed for curves by Beilinson and Drinfeld in bd, to higher-dimensional varieties. This extension entails the development of the homotopy theory of chiral and factorization structures, in a sense analogous to Quillen's homotopy theory of differential graded Lie algebras. We prove the equivalence of higher-dimensional chiral and factorization algebras by embedding factorization algebras into a larger category of chiral commutative coalgebras, then realizing this interrelation as a chiral form of Koszul duality. We apply these techniques to rederive some fundamental results of bd on chiral enveloping algebras of ⋆-Lie algebras.