Hidden Isometry in a Chiral Gauged WZW Model

It is shown that the asymmetric chiral gauging of the WZW models give rise to consistent string backgrounds. The target space structure of the [SL(2,R)/SO(1, 1)]L ⊗ [SL(2,R)/U(1)]R model is analyzed and the presence of a hidden isometry in this background is demonstrated. A nonlinear coordinate transformation is obtained which transforms the asymmetric model to the symmetric one, analyzed recently by two of the present authors. IP/BBSR/92-67 IISc-CTS/8-92 September,1992 Various techniques have been recently devised for studying and generating large number of classical solutions of [1, 2, 3] string theory. The solutions obtained by gauging [4, 5, 6] of the WZW models have been quite popular, since they provide an exact string theory generalization of many of the nontrivial solutions of general relativity. An exact conformal field theory describing a two dimensional black hole [7] can be obtained by gauging the axial or vector U(1) subgroup of an SL(2, R) WZW model [4]. Several interesting generalizations of this model have been reported [5, 6]. In general, the resulting background obtained by gauging still has residual isometries. Most often these isometries, like translations, can be obtained by a simple observation of the background configuration. It has been shown that for d-isometries, acting as translations on the coordinates, the string effective action (SEA) is invariant under an O(d, d) group [1, 2] of transformations. These transformations are useful in relating those classical solutions with each other which depend on the same number of coordinates. These symmetries manifest themselves in terms of the conserved currents on the string worldsheet. In this paper, we show that another gauging, namely the chiral gauging [8, 9, 10], can be used in left-right asymmetric manner for the construction of consistent string backgrounds. We explicitly work out the case of the asymmetric chiral gauged [SL(2,R)/SO(1, 1)]L ⊗ [SL(2,R)/U(1)]R model. The resulting target space has an isometry acting as translation. However, unlike