Duality Symmetries from Non--Abelian Isometries in String Theories

TL;DR

This paper extends target space duality in string theory from abelian to non-abelian isometries, revealing that dualities can relate spaces with no isometries, including black hole solutions, thus broadening the understanding of symmetries in string backgrounds.

Contribution

It introduces a formalism for non-abelian duality in string theory, showing that dual backgrounds can lack isometries and providing explicit examples involving black hole solutions.

Findings

Duality maps spaces with non-abelian isometries to spaces with no isometries.

New dual backgrounds include black hole solutions with naked singularities.

Some dual backgrounds have only time translation symmetry.

Abstract

In string theory it is known that abelian isometries in the sigma model lead to target space duality. We generalize this duality to backgrounds with non--abelian isometries. The procedure we follow consists of gauging the isometries of the original action and constraining the field strength $F$ to vanish. This new action generates dual theories by integrating over either the Lagrange multipliers that set F=0 or the gauge fields. We find that this new duality transformation maps spaces with non--abelian isometries to spaces that may have no isometries at all. This suggests that duality symmetries in string theories need to be understood in a more general context without regard to the existence of continuous isometries on the target space (this is also indicated by the existence of duality in string compactifications on Calabi--Yau manifolds which have no continuous isometries). Physically interesting examples to which our formalism apply are the Schwarzschild metric and the 4D charged dilatonic black hole. For these spherically symmetric black holes in four dimensions, the dual backgrounds are presented and explicitly shown to be new solutions of the leading order string equations. Some of these new backgrounds are found to have no continuous isometries (except for time translations) and also have naked singularities.