Semiclassical vs. Exact Solutions of Charged Black Hole in Four Dimensions and Exact O(d,d) Duality

Abstract

We derive a charged black hole solution in four dimensions described by $SL(2,R)\times SU(2)\times U(1)/U(1{)}^2$ WZW coset model. Using the algebraic Hamiltonian method we calculate the corresponding solution that is exact to all orders in $\frac{1}{k}$. It is shown that unlike the 2D black hole, the singularity remains also in the exact solution, and moreover, in some range of the gauge parameter the space-time does not fulfil the cosmic censor conjecture, $i.e.$ we find a naked singularity outside the black hole. Exact dual models are derived as well, one of them describes a 4D space-time with a naked singularity. Using the algebraic Hamiltonian approach we also find the exact to all orders $O(d,d)$ transformation of the metric and the dilaton field for general WZW coset models and show the correction with respect to the transformations in one loop order.

42 pages, (typographical errors in pages 33 and 35)

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• A Conformal Field Theory of a Rotating Dyon
• Exact O(d,d) Transformations in WZW Models
• On the Geometry of Coset Models with Flux
• SU(3)_c X SU(4)_L X U(1)_x model for three families