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In the past couple years, I've read many words pertaining to D-branes without feeling I have really comprehended them. In broad terms, I think I get what they're about: They're supposed to serve as habitats for the ends of open strings and can be viewed as submanifolds (of the target manifold in a sigma model), possibly augmented with a vector bundle, or a sheaf of [somethings], or maybe some other kind of label. (Please correct me if I got that wrong.)

In the hopes of tightening my grasp on the concept, here are some of the questions that have been nagging me during my reading.

  1. What specifically is the definition of a D-brane, say in the context of a topological field theory? (Or what are the most promising provisional definitions?) What references are most accessible to a mathematical audience?
  2. What picture should I have in my head when an author talks about "the moduli space of D-branes"?
  3. What is the idea behind the "dynamics of D-branes" that researchers sometimes talk about? (Perhaps when I understand better how to think about these gadgets, it will be easier to conceive of how they should change over time.)
  4. What goes into verifying (or at least asserting/conjecturing) that the elements of twisted K-theory classify D-brane charges?

(I considered putting this on MO, but it feels too basic relative to what TFT people talk about there for it to be appropriate.)

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