Branes and quantization

Abstract

The problem of quantizing a symplectic manifold (M,ω) 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,ω) is the space of (B_(cc), B) strings, where B_(cc) 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 ω is encoded in the choice of B_(cc). 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.

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