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

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.