Correlation functions of symmetric orbifold from AdS3 string theory

The paper examines correspondence among correlation functions of symmetric orbifold and string theory on AdS3 described by sl(2) Wess-Zumino-Novikov-Witten (WZNW) model. We start by writing down n-point function of twist operators in the symmetric orbifold in terms of the data of effective Riemann surface. It is then shown that the correlation function can be reproduced from the sl(2) WZNW model. The computation is based on the claim that string worldsheet is given by the same Riemann surface and the reduction method from sl(2) WZNW model to Liouville field theory. We first consider the genus zero surface and then generalize the analysis to the case of generic genus. The radius of AdS3 is related to the level k of the WZNW model. For k = 3, our result should be an important ingredient for deriving AdS3/CFT2 correspondence with tensionless superstrings to all orders in string perturbation theory. For generic k, relations involving specific forms of correlation functions for strings on AdS3× X were obtained.

LANGLANDS DUALITY IN LIOUVILLE-$H^3_+$ WZNW CORRESPONDENCE

We show a physical realization of the Langlands duality in correlation functions of [Formula: see text] WZNW model. We derive a dual version of the Stoyanovky–Riabult–Teschner (SRT) formula that relates the correlation function of the [Formula: see text] WZNW and the dual Liouville theory to investigate the level duality k - 2 → (k - 2)-1 in the WZNW correlation functions. Then, we show that such a dual version of the [Formula: see text]-Liouville relation can be interpreted as a particular case of a biparametric family of nonrational conformal field theories (CFT's) based on the Liouville correlation functions, which was recently proposed by Ribault. We study symmetries of these new nonrational CFT's and compute correlation functions explicitly by using the free field realization to see how a generalized Langlands duality manifests itself in this framework. Finally, we suggest an interpretation of the SRT formula as realizing the Drinfeld–Sokolov Hamiltonian reduction. Again, the Hamiltonian reduction reveals the Langlands duality in the [Formula: see text] WZNW model. Our new identity for the correlation functions of [Formula: see text] WZNW model may yield a first step to understand quantum geometric Langlands correspondence yet to be formulated mathematically.