String correlators in AdS3 from FZZ duality

Motivated by recent works in which the FZZ duality plays an important role, we revisit the computation of correlation functions in the sine-Liouville field theory. We present a direct computation of the three-point function, the simplest to the best of our knowledge, and give expressions for the N-point functions in terms of integrated Liouville theory correlators. This leads us to discuss the relation to the $$ {H}_3^{+} $$ H 3 + WZW-Liouville correspondence, especially in the case in which spectral flow is taken into account. We explain how these results can be used to study scattering amplitudes of winding string states in AdS3.

Higher rank FZZ-dualities

We examine strong/weak dualities in two dimensional conformal field theories by generalizing the Fateev-Zamolodchikov-Zamolodchikov (FZZ-)duality between Witten’s cigar model described by the $$ \mathfrak{sl}(2)/\mathfrak{u}(1) $$ sl 2 / u 1 coset and sine-Liouville theory. In a previous work, a proof of the FZZ-duality was provided by applying the reduction method from $$ \mathfrak{sl}(2) $$ sl 2 Wess-Zumino-Novikov-Witten model to Liouville field theory and the self-duality of Liouville field theory. In this paper, we work with the coset model of the type $$ \mathfrak{sl}\left(N+1\right)/\left(\mathfrak{sl}(N)\times \mathfrak{u}(1)\right) $$ sl N + 1 / sl N × u 1 and investigate the equivalence to a theory with an $$ \mathfrak{sl}\left(N+\left.1\right|N\right) $$ sl N + 1 N structure. We derive the duality explicitly for N = 2, 3 by applying recent works on the reduction method extended for $$ \mathfrak{sl}(N) $$ sl N and the self-duality of Toda field theory. Our results can be regarded as a conformal field theoretic derivation of the duality of the Gaiotto-Rapčák corner vertex operator algebras Y0,N,N+1[ψ] and YN,0,N+1[ψ−1].

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.