DISENTANGLING NONABELIAN DISCRETE QUANTUM HAIR

Last year, Krauss and Wilczek studied a theory in which a U(1) gauge group broke down to a discrete Z(N) subgroup. They argued that despite the classical no-hair theorems, the Z(N) charge carried by a black hole was an observable quantity, "discrete quantum hair". In this note we extend their analysis to the case in which a general continuous gauge group G breaks down to a discrete nonabelian subgroup H. We find that the H-transformation properties of a black hole are (with one minor exception) as observable as those of any other particle. Just as in the Z(N) case, the observations are made by gedanken experiments involving the interactions of black holes and cosmic strings. To complete the argument we have to investigate the quantum theory of nonabelian cosmic strings. We find (somewhat surprisingly) that one should not expect to find cosmic strings in states that correspond to irreducible representations of H.