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

TL;DR

This paper explores the formulation of string theory in AdS_3 as a marginal deformation of a linear dilaton background, connecting it with Liouville and sine-Liouville theories to better understand string interactions and spectra.

Contribution

It introduces a free field representation of AdS_3 string theory as a marginal deformation, linking it to Liouville and sine-Liouville models for the first time.

Findings

Unified description of correlators in Liouville and WZNW theories.

Clarification of the spectrum and interactions of strings in Lorentzian AdS_3.

Connection between different realizations of AdS_3 string theory.

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.