Simplicity of AdS Super Yang-Mills at One Loop

TL;DR

This paper systematically analyzes one-loop Mellin amplitudes for super gluons in AdS5×S3, revealing remarkable simplicity and extending understanding of hidden conformal symmetry beyond previous limits.

Contribution

It provides general expressions for four-point one-loop Mellin amplitudes in AdS5×S3 and uncovers new insights into their pole structure and hidden symmetries.

Findings

Amplitudes contain only simultaneous poles in two Mellin variables.

Extended the implications of eight-dimensional hidden conformal symmetry.

Identified a small finite set of poles determined by protected operators.

Abstract

We perform a systematic bootstrap analysis of four-point one-loop Mellin amplitudes for super gluons in $\mathrm{AdS}_5\times\mathrm{S}^3$ with arbitrary Kaluza-Klein weights. The analysis produces the general expressions for these amplitudes at extremalities two and three, as well as analytic results for many other special cases. From these results we observe remarkable simplicity. We find that the Mellin amplitudes always contain only simultaneous poles in two Mellin-Mandelstam variables, extending a previous observation in the simplest case with the lowest Kaluza-Klein weights. Moreover, we discover a substantial extension of the implication of the eight-dimensional hidden conformal symmetry, which goes far beyond the Mellin poles associated with the leading logarithmic singularities. This leaves only a small finite set of poles which can be determined on a case-by-case basis from the contributions of protected operators in the OPE.