Conformally Exact Metric and Dilaton in String Theory on Curved Spacetime

Abstract

Using a Hamiltonian approach to gauged WZW 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 non-supersymmetric {\it semi-classical} bosonic model except for an overall renormalization of the metric obtained by $k\to k-g$. (ii) The exact expressions for the heterotic superstring are derived from their exact bosonic string counterparts by shifting the central extension $k\to 2k-h$ (but an overall factor $(k-g)$ remains unshifted). (iii) The combination $e^{\Phi }\sqrt{-G}$ is independent of $k$ and therefore can be computed in lowest order perturbation theory as required by the correct formulation of a conformally invariant path integral measure. 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 $(k\to \infty )$ our results agree with those obtained with the Lagrangian method up to 1-loop in perturbation theory.

USC-92/HEP-B2, 19 pages and 3 figures

References in corpus (7)

• Elements of String Cosmology
• Cosmological String Backgrounds from Gauged WZW Models
• Generalized Duality and Singular Strings in Higher Dimensions
• A Superstring Theory in Four Curved Space-Time Dimensions
• Some Exact Solutions of String Theory in Four and Five Dimensions
• Global Analysis of New Gravitational Singularities in String and Particle Theories
• Exact Solutions of Four Dimensional Black Holes in String Theory

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