CONFORMALLY EXACT METRIC AND DILATON IN STRING THEORY ON CURVED SPACETIME

Using a Hamiltonian approach to gauged Wess-Zumino-Witten models, we present a general method for computing the conformally exact metric and dilaton, to all orders in the 1/k expansion, for any bosonic, heterotic, or type-II superstring model based on a coset G/H. We prove the following relations: (i) For type-II superstrings the conformally exact metric and dilaton are identical to those of the nonsupersymmetric semiclassical bosonic model except for an- overall renormalization of the metric obtained by k --> k - g. (ii) The exact expressions for the heterotic superstring are derived from their exact bosonic string counterparts by shifting the central extension k --> 2k - h [but an overall factor (k -g) remains unshifted]. (iii) The combination e(phi) square-root - G is independent of k and therefore can be computed in lowest-order perturbation theory. The general formalism is applied to the coset models SO(d - 1,2)-k/SO(d - 1, 1)-k that are relevant for string theory on curved spacetime. Explicit expressions for the conformally exact metric and dilaton for the cases d =2,3,4 are given. In the semiclassical limit (k --> infinity) our results agree with those obtained with the Lagrangian method up to one loop in perturbation theory.