Chern-Simons forms, Mickelsson-Faddeev algebras and the p-branes

Abstract In string theory, nilpotence of the BRS operator δ for the string functional relates the Chern-Simons term in the gauge-invariant antisymmetric tensor field strength to the central term in the Kac-Moody algebra. We generalize these ideas to p -branes with odd p and find that the Kac-Moody algebra for the string becomes the Michelsson-Faddeev algebra for the p -brane.