Gauge Symmetries of the N=2 String

We study the underlying gauge symmetry algebra of the N = 2 string, which is broken down to a subalgebra in any spacetime background. For given toroidal backgrounds, the unbroken gauge symmetries (corresponding to holomorphic and antiholomorphic worldsheet currents) generate area-preserving diffeomorphism algebras of null 2-tori. A minimal Lie algebraic closure containing all the gauge symmetries that arise in this way, is the background–independent volume–preserving diffeomorphism algebra of the target Narain torus T . The underlying symmetries act on the ground ring of functions on T 4,4 as derivations, much as in the case of the d = 2 string. A background–independent spacetime action valid for noncompact metrics is presented, whose symmetries are volume– preserving diffeomorphisms. Possible extensions to N = 2 and N = 1 heterotic strings are briefly discussed.