Duality Symmetries from Non–Abelian Isometries in String Theory∗

In string theory it is known that abelian isometries in the σ–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.