SUPER P-BRANES AS GAUGE-THEORIES OF VOLUME PRESERVING DIFFEOMORPHISMS

We obtain the light-cone gauge-fixed action for a super p-brane. For p = 2 it is known that the action is equivalent to that of a one-dimensional super-Yang-Mills theory of the (infinite dimensional) area preserving diffeomorphism group of the membrane. We show that for p > 2 the action is that of a new kind of supersymmetric gauge theory of p-volume-preserving diffeomorphisms that is not of Yang-Mills type, and we conjecture that it is related to an infinite-dimensional non-Abelian antisymmetric tensor gauge theory. We compute the classical algebra of the supersymmetry charges and generators of the volume preserving diffeomorphisms, and show that it does not allow central extensions. © 1990.