The String Theory on AdS_3 as a Marginal Deformation of a Linear Dilaton Background

Abstract

We investigate N-point string scattering amplitudes in AdS_3 space. Based on recent observations on the solutions of KZ and BPZ-type differential equations, we discuss how to describe the string theory in AdS_3 as a marginal deformation of a (flat) linear dilaton background. This representation resembles the called "discrete light-cone Liouville" realization as well as the FZZ dual description in terms of the sine-Liouville field theory. Consequently, the connection and differences between those and this realization are discussed. The free field representation presented here permits to understand the relation between correlators in both Liouville and WZNW theories in a very simple way. Within this framework, we discuss the spectrum and interactions of strings in Lorentzian AdS_3.

30 pages, no figures. Some minor typos corrected; e.g. minor typo in Eq. (5) and Eq. (23)

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• Langlands duality in Liouville-H_3^+ WZNW correspondence
• String correlators in AdS${}_3$ from FZZ duality
• Stringy horizons and generalized FZZ duality in perturbation theory
• Topological String on OSP(1|2)/U(1)
• A Note on Z_2 Symmetries of the KZ Equation
• Disk one-point function for non-rational conformal theories
• Three-Point Function in Perturbed Liouville Gravity
• Conformal field theories from deformations of theories with $W_n$ symmetry
• Attached Open Strings on a D$p$-brane in the Backgrounds of the pp-wave and Linear Dilation