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 T4,4. The underlying symmetries act on the ground ring of functions on T4,4 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.
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We thank B. Greene, A. leClair, R. Plesser, M. Ro~ek,D. Spector, H. Tye, E. Verlinde, E. Witten, and B. Zwiebach for discussions. The work of A.G. is supported in part by DOE grant no. DE-FGO2-90ER40542. A.S. is supported in part by NSF grant no. PHY-87-15272.