String Theory on AdS_3 as Discrete Light-Cone Liouville Theory

TL;DR

This paper reformulates string theory on $AdS_3$ as a linear dilaton theory with a light-like compactification, revealing a spectrum of chiral primaries and connections to the $AdS_3/CFT_2$ duality and long string configurations.

Contribution

It introduces a novel reformulation of $AdS_3$ string theory as a discrete light-cone Liouville theory, linking spectral flow, long strings, and the symmetric orbifold model.

Findings

Identification of discrete light-cone momentum with winding number

Existence of infinite chiral primary states with spectral flow

Spectrum consistent with $AdS_3/CFT_2$ duality

Abstract

We investigate (super) string theory on $AdS_3$ background based on an approach of free field realization. We demonstrate that this string theory can be reformulated as a string theory defined on a linear dilaton background along the transverse direction (``Liouville mode'') and compactified onto $S^1$ along a {\em light-like} direction. Under this reformulation we analyze the physical spectrum as that of a free field system, and discuss the consequences when we turn on the Liouville potential. The discrete light-cone momentum in our framework is naturally interpreted as the ``winding number'' of the long string configuration and is identified with the spectral flow parameter that is introduced in the recent work by Maldacena and Ooguri \cite{MO}. Moreover we show that there exist infinite number of the on-shell chiral primary states possessing the different light-cone momenta and the spectral flow consistently acts on the space of chiral primaries. We observe that they are also chiral primaries in the sense of space-time (or the conformal theory of long string) and the spectrum of space-time $U(1)_R$ charge is consistent with the expectation from the $AdS_3/CFT_2$-duality. We also clarify the correspondence between our framework and the symmetric orbifold theory of multiple long string system \cite{HS2}.