$20'$ Five-Point Function of $\mathcal{N}=4$ SYM and Stringy Corrections

TL;DR

This paper develops a bootstrap method to compute stringy corrections to five-point functions in N=4 SYM, refining previous models and verifying consistency with flat-space limits.

Contribution

It introduces a novel bootstrap approach that constrains stringy corrections to five-point correlators using Mellin amplitudes and supersymmetry, reducing ambiguity to a single coefficient.

Findings

Computed the first stringy correction to five-point functions of 20' operators.

Identified non-protected CFT data sensitive to the correction's ambiguity.

Verified the correction's compatibility with flat-space Mellin amplitude behavior.

Abstract

We set up a bootstrap approach to compute the first stringy correction to the supergravity regime of the correlation function of five 20' operators in $\mathcal{N}=4$ super Yang-Mills. We use factorization of Mellin amplitudes, supersymmetric constraints and protected observables to refine our ansatz, leaving only a single undetermined coefficient. We identify non-protected CFT data that is sensitive to the residual ambiguity of our ansatz, and we verify the compatibility of our result with the anticipated behaviour of the Mellin amplitude in the flat-space limit. As a byproduct of our analysis, we also compute the first stringy correction to the four-point correlators of three 20' operators and either one R-symmetry current or one stress tensor.