Séminaire de Physique Théorique

Higher chiral differential operators

by Prof. Brian WILLIAMS (Northwestern University & IHES)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


35, route de Chartres, F-91440 Bures-sur-Yvette (France)
The sheaf of chiral differential operators is a sheaf of vertex algebras defined by Gorbounov, Malikov, and Schechtman in the early nineties that exists on any manifold with vanishing second component of its Chern character. Later on it was proposed by Witten to be related to the chiral operators of the (0,2)-supersymmetric sigma-model. Recently, we have proved this using an approach to QFT developed by Costello: the BV-quantization of the holomorphic twist of the (0,2) theory is isomorphic to the sheaf of chiral differential operators. Along with Gorbounov and Gwilliam, we prove this using the language of holomorphic factorization algebras in one complex dimension. In this talk I will sketch the proof of this result while also motivating a family of BV theories that produce sheaves of higher dimensional holomorphic factorization algebras that deserve to be called “higher” CDOs. We discuss the meaning of the OPE for these theories as encoded by the higher dimensional factorization structure.