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Quantum statistics of branes

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Quantum statistics of particles (bosons, fermions, anyons) arises due to the possible topologies of curves in D-dimensional spacetime winding around each other

What happens if we replace particles by branes? It seems like their quantum statistics should be described by something like a generalization of TQFT in which the "spacetime" (worldbrane) is equipped with an embedding into an "ambient" manifold (actual spacetime). The inclusion of non-trivial topology for the "ambient" manifold introduces additional effects, to 1st approximation describable by inclusion of k-form fluxes coupling to the brane. To 2nd approximation, however, there is probably non-trivial coupling between these fluxes and the "generalized quantum statistics"

A simple example of non-trivial "brane quantum statistics" is the multiplication of quantum amplitudes of strings by the exponential of the euler charactestic times a constant. In string theory this corresponds to changing the string coupling constant / dilaton background.

Were such generalized TQFTs studied? Which non-trivial examples are there for branes in string theory?

This post has been migrated from (A51.SE)
asked Dec 2, 2011 in Theoretical Physics by Squark (1,700 points) [ no revision ]
You are probably aware of this, but just for completeness: N coincident branes have a U(N) gauge symmetry, which is broken to $U(1)^N\times S_N$ when they are separated. The permutation symmetry $S_N$ is a discrete gauge symmetry which ensures branes are treated as identical particles. Your question seems related to which kind of identical particles they are (bosons, fermions, or anyons).

This post has been migrated from (A51.SE)

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