Types of quantum field thories
More in detail, the symplectic manifold serves as the target space for the 2-dimensional sigma-model TQFT called the A-model. If the symplectic manifold arises as the complexification of a phase space of some physical system, then one finds that the boundary path integral of the A-model on cosiotropic branes computes the path integral and the geometric quantization of this physical system.
The goal is to get closer to a systematic theory of quantization.
The main original article is
Earlier, suggestions that the A-model is related to deformation quantization had been given in
which then have been extended and made more precise in
in the context of generalized complex geometry.
Tha the space of states of open strings in the A-model can be interpreted as a quantization of the corresponding symplectic manifold had first been noticed in examples in
The canonical coisotropic brane was used to elucidate these matters further in
is the context of the Kapustin-Witten TQFT.
A relation to the path integral is discussed in