All Tree-Level Correlators in AdS${}_5\times$S${}_5$ Supergravity: Hidden Ten-Dimensional Conformal Symmetry

TL;DR

This paper uncovers a hidden ten-dimensional conformal symmetry in tree-level supergravity correlators on AdS${}_5\times$S${}_5$, leading to simplified expressions and confirming conjectured anomalous dimension patterns.

Contribution

It reveals a novel ten-dimensional conformal symmetry in supergravity correlators, unifying spherical harmonics and simplifying the computation of correlators at all loop orders.

Findings

Confirmed the pattern of double-trace anomalous dimensions.

Derived compact expressions for correlators using the symmetry.

Validated the symmetry through analytic bootstrap methods.

Abstract

We study correlators of four protected (half-BPS) operators in strongly coupled supersymmetric Yang-Mills theory. These are dual to tree-level supergravity amplitudes on AdS${}_5\times$S${}_5$ for various spherical harmonics on the five-sphere. We use conformal field theory methods, in particular a recently obtained Lorentzian inversion formula, to analytically bootstrap these correlators. The extracted $1/N^2$ double-trace anomalous dimensions confirm a simple pattern recently conjectured by Aprile, Drummond, Heslop and Paul. We explain this pattern by an unexpected ten-dimensional conformal symmetry which appears to be enjoyed by tree-level supergravity (or a suitable subsector of it). The symmetry combines all spherical harmonics into a single ten-dimensional object, and yields compact expressions for the leading logarithmic part of any half-BPS correlator at each loop order.