Gauge symmetries of the N = 2 string

Abstract

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 4,4. 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.