Black Holes from Non-Abelian Toda Theories

TL;DR

This paper demonstrates that non-abelian Toda theories can model exactly solvable conformal systems with black hole backgrounds, offering new insights into string propagation in such curved spacetimes.

Contribution

It introduces a class of non-abelian Toda theories associated with non-canonical gradations, expanding the scope of exactly solvable models with black hole solutions.

Findings

Exact solutions for black hole backgrounds in non-abelian Toda theories

Connection between gauged WZNW models and black hole conformal systems

Classical integrability of the non-abelian Toda potential

Abstract

NON-ABELIAN TODA THEORIES are shown to provide EXACTLY SOLVABLE conformal systems in the presence of a BLACK HOLE which may be regarded as describing a string propagating in target space with a black-hole metric. These theories are associated with non-canonical $\bf Z$-gradations of simple algebras, where the gradation-zero subgroup is non-abelian. They correspond to gauged WZNW models where the gauge group is nilpotent and are thus basically different from the ones currently considered following Witten. The non-abelian Toda potential gives a cosmological term which may be exactly integrated at the classical level.