Zero modes of non-abelian vortices

Abstract

We investigate the bosonic zero modes of cosmic strings formed in the breaking of a gauge group G → H, and find exact charge-carrying zero mode solutions. For the case of G = U ̄ (1) × U(1) we find that it is necessary to modify Witten's superconducting zero mode ansatz. In the case of non-abelian G, zero modes are generically present. Further, in the presence of a non-abelian string the embedding of H in G is angle dependent, with only a subgroup H̄ being globally single valued. This subgroup is determined by the Wilson loop integral around the string, and depends on detailed dynamics. We find that gauge bosons associated with multivalued generators Aharonov-Bohm scatter off the string. The Alice string ( H = O(2), H ̄ = Z 2 ) has novel electrodynamics: it attracts charges, scatters the SO(2) “photon”, and a two-string system has zero modes with unlocalizable (“Cheshire”) charge. We extend this analysis to generalized Alice strings and end by considering the bosonic zero modes of domain walls.