Non-Abelian statistics of vortices with non-Abelian Dirac fermions

Details Non-Abelian statistics of vortices with non-Abelian Dirac fermions Non-Abelian statistics of vortices with non-Abelian Dirac fermions

2012-04-05

arxiv.org/abs/1204.1164v1

Physics

Condensed Matter

Superconductivity

Scientific paper

We extend our previous analysis on the exchange statistics of vortices having a single Dirac fermion trapped in each core, to the case where vortices trap two Dirac fermions with U(2) symmetry. Such a system of vortices with non-Abelian Dirac fermions appears in color superconductors at extremely high densities, and in supersymmetric QCD. We show that the exchange of two vortices having doublet Dirac fermions in each core is again non-Abelian, which is explicitly verified in the matrix representation of the exchange operators when the number of vortices is up to four. We find that the result contains the matrices previously obtained for the vortices with a single Dirac fermion in each core as a special case.

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