Description:

Title: Higher rank brane quantization of Kaehler manifolds

Abstract:  Consider a spin Kaehler manifold M with a prequantum line bundle L. Gukov-Witten suggested that, with respect to the A-model on a complexification X of M, the morphism spaces Hom(Bcc, Bcc) and Hom(B, Bcc) should recover holomorphic deformation quantization of X and geometric quantization of M respectively, where Bcc is a canonical coisotropic A-brane on X and B is a Lagrangian A-brane supported on M.
On the other hand, Chan-Leung-Li adopted Fedosov's gluing argument to construct a dense subsheaf Oqu of smooth functions on M with a non-formal star product and a left Oqu-module structure on the sheaf of holomorphic sections of the tensor product of kth tensor power of L and a square root of the canonical bundle of M.
In this talk, I will discuss the relation between (holomorphic) deformation quantizations of M and a sufficiently small complexification X so as to verify that Chan-Leung-Li's construction provides a mathematical realization of the action of Hom(Bcc, Bcc) on Hom(B, Bcc). I will also introduce a categorification of their construction and propose that it serves as part of the categorical structures on higher rank coisotropic A-branes on X, motivated by Kuwagaki's idea of sheaf quantization.

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