$\mathbf{AdS_3\times S^3}$ Tree-Level Correlators: Hidden Six-Dimensional Conformal Symmetry

Abstract

We revisit the calculation of holographic correlators in $AdS_3$. We develop new methods to evaluate exchange Witten diagrams, resolving some technical difficulties that prevent a straightforward application of the methods used in higher dimensions. We perform detailed calculations in the $AdS_3 \times S^3 \times K3$ background. We find strong evidence that four-point tree-level correlators of KK modes of the tensor multiplets enjoy a hidden 6d conformal symmetry. The correlators can all be packaged into a single generating function, related to the 6d flat space superamplitude. This generalizes an analogous structure found in $AdS_5 \times S^5$ supergravity.