Branes and quantization

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 B cc 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.