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

TL;DR

This work advances the computation of holographic four-point functions in $AdS_3$ by developing a robust position-space framework that handles exchange Witten diagrams unique to AdS$_3$, and by exploring a Mellin-space perspective. The authors provide strong evidence for a hidden six-dimensional conformal symmetry that organizes tensor multiplet KK four-point functions into a single generating function tied to the 6d flat-space superamplitude, paralleling the structure found in $AdS_5\times S^5$. They compute explicit results for low- and higher-weight correlators in the $AdS_3\times S^3\times K3$ background, and propose a concrete generating-function prescription for all KK weights, with clear distinctions between tensor and gravity multiplets. This hidden symmetry, if further understood, could streamline the determination of CFT data and guide loop-level analyses in holography across backgrounds with maximal or half-maximal supersymmetry.

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.