Branes and Quantization

Understand

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.