Are anyons possible in higher dimensions?

[haael]

Weinberg wrote that in 3D and higher spaces all particles must be bosons or fermions. The proof used the fact that particles are really indistinguishable i.e. we can't "mark" any particle and the mathematical replacement of two particles of the same type should not change any physical observable.

Yet in 2D space there anyons are possible. The particles' trajectories can nontrivially wrap over themselves and thus they are distinguishable. A particle spacetime history is its "mark". This is possible only in 2D space, since in higher dimensions all trajectories are topologically equivalent.

Now what if 3D space had some nontrivial topology? I.e. there is a wormhole or there is some elementary string or loop that particles can wrap around. This would give us the necessary topological mark so the proof does not pass.

Does anyone know if anyons can exist in higher-dimensional spaces with nontrivial topology?

 

[atyy]

Teo and Kane tried something like this: Majorana Fermions and Non-Abelian Statistics in Three Dimensions.

Stern and Levin wrote some commentary on the proposal.

 

[element4]

See also http://arxiv.org/abs/1005.0583 .