Target Space Structure of a Chiral Gauged Wess-Zumino-Witten Model

The background for string propagation is obtained by a chiral gauging of the SL(2, R) Wess-Zumino-Witten model. It is shown explicitly that the resulting background fields satisfy the field equations of the three dimensional string effective action and the target space has curvature singularity. Close connection of our solution with the three dimensional black string is demonstrated. IP/BBSR/92-18 March ’92. e-mail:supriya%[email protected] e-mail:kumar%[email protected] The target space structure of the gauged Wess-Zumino-Witten (WZW ) model has been investigated by Witten [1] and others [2]. It was shown [1] that the vector or axial gauging of a U(1) subgroup of the SL(2, R) WZW model leads to the string propagation in a two dimensional target space with black hole singularity. There have been several generalizations of this result. In particular, two dimensional charged black hole [3], three dimensional black string [4] as well as four dimensional solutions with curvature singularities [5, 6] have been constucted as gaugedWZW models. It has also been demonstrated that the two gaugings mentioned above are related by duality [7, 8] and they are anomaly free. In a recent paper [9], it has been shown that there is another gauging for the two dimensional WZW model, called ”chiral gauging”,which is also anomaly free. Quantization of the chiral WZW model and their applications to the coset constructions have been done in ref.[9]. In this paper, we investigate the target space structure of the SL(2, R) WZW model with a chiral U(1) gauging. It is shown that the resulting model describes a three dimesional target space with curvature singularity. Furthermore, by an O(2, 2) transformation acting on background metric (Gμν), dilaton (φ) and antisymmetric tensor (Bμν), it is demonstrated explicitly that our solution can be transformed to the three dimensional uncharged black string of ref.[4]. The connection to the charged black string [4] is also discussed.