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

Understand

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 expressed by non-Abelian representations of a braid group, 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.