Three Dimensional Black Holes and Four Dimensional Black Strings as Nonlinear Sigma Models

TL;DR

This paper demonstrates that certain three- and four-dimensional black hole and black string solutions in string theory are exact conformal field theories, represented as nonlinear sigma models, with implications for quantum gravity.

Contribution

It shows that these black hole and black string solutions are exact WZWN nonlinear sigma models, valid to all orders in inverse string tension, and also solve standard GR equations with a constant dilaton.

Findings

Solutions are exact conformal field theories.

They are represented as nonlinear sigma models.

Solutions also satisfy Einstein equations with a three-form field.

Abstract

Two solutions of stringy gravity in three and four dimensions which admit interpretation as a black hole and a black string, respectively, are discussed. It is demonstrated that they are exact WZWN nonlinear sigma models to all orders in the inverse string tension, and hence represent exact conformal field theories on the world-sheet. Furthermore, since the dilaton for these two solutions is constant, they also solve the equations of motion of standard GR with a minimally coupled three form field strength. (Based on a talk presented at the Conference on Quantum Aspects of Black Holes, U. of California, Santa Barbara CA June 21-27 '93, and a poster presented at 5th Canadian Conference on General Relativity and Relativistic Astrophysics, Waterloo, Ont., May 13-15, 1993.)