New realizations of the Virasoro algebra as membrane symmetries

Abstract

We construct new realizations of the Virasoro algebra as subalgebras of area preserving diffeomorphisms of surfaces, which are the membrane symmetries. For the membrane torus, the SDiff(T 2) algebra has a central extension of unique form and the corresponding Virasoro subalgebras are in general realized as non-trivial central extensions. These central extensions should be relevant to the question whether quantum string excitations may be contained in the membrane spectrum.