Remarks on single trace TT¯ and other current-current deformations

Abstract

String theory on AdS3 with NS-NS fluxes admits a solvable irrelevant deformation which is close to the TT¯ deformation of the dual conformal field theory (CFT2). This consists of deforming the world sheet action, namely the action of the SL(2,R) Wess-Zumino-Witten model, by adding to it the operator J-J¯-, constructed with two Kac-Moody currents. The geometrical interpretation of the resulting theory is that of strings on a conformally flat background that interpolate between anti-de Sitter (AdS3) in the IR and a flat linear dilaton spacetime with its Hagedorn spectrum in the UV, having passed through a transition region of positive curvature. Here, we study the properties of this string background both from the point of view of the low-energy effective theory and of the world sheet CFT. We first study the geometrical properties of the semiclassical geometry, then we revise the computation of correlation functions and of the spectrum of the J-J¯- deformed world sheet theory, and finally we discuss how to extend this type of current-current deformation to other conformal models.