Worldsheet correlators in AdS(3)/CFT(2)

TL;DR

This paper tests the AdS$_3$/CFT$_2$ correspondence beyond the supergravity limit by explicitly computing sphere-level two- and three-point functions of chiral primary operators, which correspond to $n$-cycle twist operators in the boundary symmetric orbifold CFT. By constructing the dual worldsheet chiral primaries in the ${ m SL}(2)_k imes { m SU}(2)_{k'} imes U(1)^4$ theory with $k=k'=N_5$, the authors show that the worldsheet and boundary correlators match both in functional form and normalization in the large-$N$ limit, with the sphere contribution dominating the string perturbation series. The two-point function fixes the normalization between worldsheet and boundary operators, while the three-point function provides a nontrivial consistency check of the duality, including a delicate $j$-shift and a consistent large-$N$ scaling of the coefficients. The results bolster the view that chiral primaries are protected and that full worldsheet techniques can reproduce boundary CFT data in the AdS$_3$/CFT$_2$ setting, offering a blueprint for future higher-point tests and extensions to other backgrounds.

Abstract

The AdS_3/CFT_2 correspondence is checked beyond the supergravity approximation by comparing correlation functions. To this end we calculate 2- and 3-point functions on the sphere of certain chiral primary operators for strings on AdS_3 x S^3 x T^4. These results are then compared with the corresponding amplitudes in the dual 2-dimensional conformal field theory. In the limit of small string coupling, where the sphere diagrams dominate the string perturbation series, beautiful agreement is found.