Quantization of Kapranov $L_\infty$ structure and Bargmann-Fock sheaves on Kahler manifolds

Abstract: In this talk, I will introduce a quantization of Kapranov $L_\infty$ structure on K\"ahler manifolds, which gives rise to a special class of solutions of Fedosov equations. These solutions give rise to one-loop exact BV quantization using Costello's theory of effective renormalization. By using these Fedosov connections, we will also construct a sheaf of modules over deformation quantization algebra which we call Bargmann-Fock sheaves. This in particular give rise to a representation of Berezin-Toeplitz quantization on Hilbert spaces.

Mathematics

Audience: researchers in the topic

ICCM 2020