DISCRETE QUANTUM HAIR ON BLACK-HOLES AND THE NON-ABELIAN AHARONOV-BOHM EFFECT

In an abelian Higgs model where U(1) is broken to Zp by a condensate of charge pe, the U(1) charge QV in a finite volume V is an observable, but charge is screened, so 〈 QV 〉 falls exponentially to zero as V → ∞. It is demonstrated that the Zp charge, QV modulo pe, can be cast as a surface integral by evaluating exp( 2πiQV pe) in states containing a shell of unbroken vacuum around the volume, and its value is unaffected by the presence of the condensate inside the shell. Thus in these states QV modulo pe is not screened. This shows that black holes can indeed have Zp hair. The extension to a non-abelian discrete gauge charge is discussed, and the detection of this charge by its non-abelian Aharonov-Bohm interaction with cosmic strings is described. © 1990.