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

Johannes M. Henn; Jungwon Lim; William J. Torres Bobadilla

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arXiv · 2410.22465

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

Johannes M. Henn·Jungwon Lim·William J. Torres Bobadilla

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Abstract

We compute analytically the three-loop correlation function of the local operator $\text{tr} \, ϕ^3$ 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 $\text{tr} \, ϕ^2$ case.

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Johannes M. Henn, Jungwon Lim, William J. Torres Bobadilla. 2024-10-29. Analytic evaluation of the three-loop three-point form factor of $\operatorname{tr}ϕ^3$ in $\mathcal{N}=4$ sYM. https://arxiv.org/abs/2410.22465

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