Manifold corners and M theory

Question

I am currently trying to understand a paper by Hisham Sati on manifold corners and M theory. The background is that M theory admits manifolds with corners. One of the results in the paper is that the heterotic string theory can be viewed as a corner of some 12 dimensional manifold $Z_{12}$. I have a lot of questions but I'll limit myself to a few conceptual ones:

a) Do all string theories appear as corners on the same $Z_{12}$ manifold? How are these string theories seen as different entities?

b) I also recall a talk by Vafa where he mentions the search for more corners. What will this physically give us?

c) Is there an overall physical intuition for considering string theories to be corners of manifolds?

This post imported from StackExchange Physics at 2016-03-23 16:18 (UTC), posted by SE-user Eh-whaaa