Simplicity of Mellin amplitudes for AdS3×S3

The spectrum of half-Bogomol’nyi–Prasad–Sommerfeld (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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi>AdS</a:mi></a:mrow><a:mrow><a:mn>3</a:mn></a:mrow></a:msub><a:mo>×</a:mo><a:mrow><a:msup><a:mrow><a:mi mathvariant="normal">S</a:mi></a:mrow><a:mrow><a:mn>3</a:mn></a:mrow></a:msup></a:mrow></a:mrow></a:math>. We present formulas 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 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.