When migrating the server, I forgot to backup the yiye website, lost a lot of memories, sad. I also dumped a lot of my phd notes to dumpster anyway when I move away from Chicago, it is inevitable to let go.

If I consider coherent sheaf category as the category of B-branes, then how does it depends on the complexified Kahler parameters? One can either do it in the physical way, reading Witten, Hori etc; or one can do it in the math way, thinking about deformation of the Coh category by gerbes.

It turns out Andrei Caldararu's thesis deals exactly with B-field and twisted sheaves. Let's find out the definition.