Simplicity of Mellin amplitudes for AdS$_3 \times$S$^3$

TL;DR

This work shows that tree-level four-point correlators of half-BPS operators in the D1-D5 SCFT$_2$ dual to $AdS_3\times S^3$ admit remarkably simple, KK-level–independent expressions when written in generalized AdS$_3\times S^3$ Mellin space. By organizing the correlators into plus and minus sectors and exploiting a six-dimensional symmetry that emerges in Mellin space, the authors derive compact building blocks and explicit all-level formulas for tensor–tensor, tensor–graviton, and graviton four-point functions. The approach unifies the 6D origin of the dual fields with the KK dynamics, yielding manifestly crossing-symmetric structures and a transparent flat-space limit. These results not only complete the tree-level graviton correlators at all KK levels but also establish a versatile formalism likely to extend to vector fields, loop corrections, and other AdS/CFT settings where higher-dimensional symmetries constrain holographic data.

Abstract

The spectrum of half-BPS single-particle operators of the D1-D5 system in the supergravity regime is dual to the spectrum of Kaluza-Klein modes of tensor and graviton multiplets in AdS$_3\times$S$^3$. We present simple formulae for all four-point tree-level correlators of scalar half-BPS primary operators in the spectrum, and in particular, we bootstrap the four-point correlator of the graviton multiplet for all KK levels. A key insight of our approach is the use of generalized Mellin space, and a decomposition of the correlators into distinct subsectors each one characterized by different on-shell constraints among the Mellin variables. The resulting Mellin amplitudes involve a small set of building blocks with manifest properties under a six-dimensional symmetry.