First of all, I am sorry for there are a bunch of questions (though all related)and may not be well framed.

What are the DT invariants in physics. When one is computing DT invariants for a Calabi-Yau manifold, what is one computing in physics?

What about the generalized (motivic) version?

Also what does the Gromov-Witten/DT correspondence (MNOP) say in terms of physics, are there (strong) physical reasons to believe such a correspondence.

Please suggest some useful references. Thanks.