One-loop amplitudes in $AdS_5\times S^5$ supergravity from $\mathcal{N}=4$ SYM at strong coupling

TL;DR

This paper develops an algorithm to compute one-loop supergravity amplitudes in AdS_5×S^5, revealing new distinctions in correlators and addressing subtle features like protected operators, advancing understanding of strong coupling dynamics in AdS/CFT.

Contribution

The paper introduces a novel algorithm for constructing one-loop supergravity amplitudes for arbitrary Kaluza-Klein states in AdS_5×S^5, including handling low twist protected operators.

Findings

Constructed explicit multi-channel correlation functions.

Demonstrated degeneracy at tree level is lifted at one-loop.

Outlined reorganizing techniques using differential operators.

Abstract

We explore the structure of maximally supersymmetric Yang-Mills correlators in the supergravity regime. We develop an algorithm to construct one-loop supergravity amplitudes of four arbitrary Kaluza-Klein supergravity states, properly dualised into single-particle operators. We illustrate this algorithm by constructing new explicit results for multi-channel correlation functions, and we show that correlators which are degenerate at tree level become distinguishable at one-loop. The algorithm contains a number of subtle features which have not appeared until now. In particular, we address the presence of non-trivial low twist protected operators in the OPE that are crucial for obtaining the correct one-loop results. Finally, we outline how the differential operators $\widehat{\mathcal{D}}_{pqrs}$ and $\Delta^{(8)}$, which play a role in the context of the hidden 10d conformal symmetry at tree level, can be used to reorganise our one-loop correlators.