U(1)-extended gauge algebras in p-loop space

Abstract

We consider, for p odd, a p-brane coupled to a (p + 1)th-rank background antisymmetric tensor field and to background Yang-Mills (YM) fields via a Wess-Zumino term. We obtain the generators of antisymmetric tensor and Yang-Mills gauge transformations acting on p-brane wave functionals (functions on . The Yang-Mills generators do not form a closed algebra by themselves; instead, the algebra of Yang-Mills and antisymmetric tensor generators is a U(1) extension of the usual algebra of Yang-Mills gauge transformations. We construct the p-brane's hamiltonian and thereby find gauge-covariant functional derivatives acting on p-brane wave functionals that commute with the YM and U(1) generators.