String Theory on AdS_3 as Discrete Light-Cone Liouville Theory

Details String Theory on AdS_3 as Discrete Light-Cone Liouville Theory String Theory on AdS_3 as Discrete Light-Cone Liouville Theory

2000-05-08

arxiv.org/abs/hep-th/0005065v3

Nucl.Phys. B589 (2000) 134-166

Physics

High Energy Physics

High Energy Physics - Theory

41 pages, no figure, the version to appear in Nucl. Phys. B. Section 3 and 4 are improved, and a discussion about the multiple

Scientific paper

10.1016/S0550-3213(00)00529-0

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}.

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