Suppose the internal manifold in a string compactification of type II, say, contains a D-brane wrapped around a given cycle. Is there an obstruction to the brane changing its wrapping cycle via a sort of tunneling? I have not seen this discussed in Polchinski or Johnson. The classical motion of the brane cannot lead to something like that, evidently. Also, could the backreaction of space play a role here?
My guess is that there would be a topological reason for the stability of a D-brane as wrapping that particular cycle. I am asking this question so as to clarifiy my basic notions of D-branes, which I have only recently began to study more carefully.
