Branes and Quantization

TL;DR

This paper presents a novel perspective on quantization of symplectic manifolds using the A-model in string theory, linking it to branes and string states, with applications to group representations and gauge theory.

Contribution

It introduces a new approach to quantization via A-branes and string theory, connecting geometric quantization with string-theoretic objects and methods.

Findings

Reformulation of quantization in terms of Bcc and B' branes

Application to representations of SL(2,R)

Insights into Chern-Simons gauge theory

Abstract

The problem of quantizing a symplectic manifold (M,\omega) can be formulated in terms of the A-model of a complexification of M. This leads to an interesting new perspective on quantization. From this point of view, the Hilbert space obtained by quantization of (M,\omega) is the space of (Bcc,B') strings, where Bcc and B' are two A-branes; B' is an ordinary Lagrangian A-brane, and Bcc is a space-filling coisotropic A-brane. B' is supported on M, and the choice of \omega is encoded in the choice of Bcc. As an example, we describe from this point of view the representations of the group SL(2,R). Another application is to Chern-Simons gauge theory.