Duality symmetries from non-abelian isometries in string theory

Abstract

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.

Global aspects of T-duality, gauged sigma models and T-folds

“…The results of [28] suggest that T-duality should generalise to this case, but the non-abelian structure leads to issues similar to those that arise in non-abelian duality [36], [37], [38], so that the approach used here appears difficult to implement in that case.…”

Duality and global symmetries

“…Consider the σ-model action (1) and assume that the target space metric has a group G of non-abelian isometries [10], [33], [34], [35]. In this case, Q MN does depend on X m and transforms accordingly under X m → g m n X n , g ∈ G. We gauge the symmetry corresponding to a subgroup…”

“…Later on, this duality was understood in terms of the standard duality of 2D non-linear sigma models studied in supergravity [8] , [9] and it was extended to more general backgrounds, including backgrounds with non-abelian isometries [10]. Duality originating from symmetries of the string 2D sigma model is presently known as T -duality.…”

Target space duality I: general theory

“…The correct dual model was first found by Fridling and Jevicki [6] and Fradkin and Tseytlin [7] using path integral methods. String theory motivated a renewed interest in abelian and nonabelian duality [8,9,10,11,12,13,14,15]. It was shown that the duality transformation was canonical [16,17] and these ideas were generalized in a variety of ways [18,19,20,21,22].…”