Conformally Exact Results for SL(2,R)\times SO(1,1)^{d-2}/SO(1,1) Coset Models

TL;DR

This paper derives exact metrics and dilaton fields for specific coset models, revealing their geometric structures, singularities, and black hole/string properties, including scattering and Hawking radiation features.

Contribution

It provides conformally exact solutions for SL(2,R) and SO(1,1) coset models, including black hole and black string geometries, with detailed analysis of singularities and scattering.

Findings

Exact metrics and dilaton fields for the models.

Identification of two distinct space-time geometries.

Calculation of scattering coefficients and Hawking temperature.

Abstract

Using the conformal invariance of the $SL(2,R)\otimes SO(1,1)^{d-2}/SO(1,1)$ coset models we calculate the conformally exact metric and dilaton, to all orders in the $1/k$ expansion. We consider both vector and axial gauging. We find that these cosets represent two different space--time geometries: ($2d$ black hole)$\otimes \IR^{d-2}$ for the vector gauging and ($3d$ black string)$\otimes \IR^{d-3}$ for the axial one. In particular for $d=3$ and for the axial gauging one obtains the exact metric and dilaton of the charged black string model introduced by Horne and Horowitz. If the value of $k$ is finite we find two curvature singularities which degenerate to one in the semi--classical $k\to \infty$ limit. We also calculate the reflection and transmission coefficients for the scattering of a tachyon wave and using the Bogoliubov transformation we find the Hawking temperature.