Analytic evaluation of the three-loop three-point form factor of $\mathrm{tr}{\varphi }^3$ in $\mathcal{N}=4$ sYM

Abstract

We compute analytically the three-loop correlation function of the local operator $\text{tr}{\varphi }^3$ inserted into three on-shell states, in maximally supersymmetric Yang-Mills theory. The result is expressed in terms of Chen iterated integrals. We also present our result using generalised polylogarithms, and evaluate them numerically, finding agreement with a previous numerical result in the literature. We observe that the result depends on fewer kinematic singularities compared to individual Feynman integrals. Furthermore, upon choosing a suitable definition of the finite part, we find that the latter satisfies powerful symbol adjacency relations similar to those previously observed for the $\text{tr}{\varphi }^2$ case.

Comments: 17 pages, 4 figures, 4 tables, 680 integrals