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<p>We compute analytically the three-loop correlation function of the local operator tr <i>ϕ</i><sup>3</sup> 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 tr <i>ϕ</i><sup>2</sup> case.</p>

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Analytic evaluation of the three-loop three-point form factor of tr ϕ3 in \( \mathcal{N} \) = 4 sYM

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  • 发表日期：

    2025年2月12日

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  • Johannes M. Henn,
  • Jungwon Lim,
  • William J. Torres Bobadilla

摘要

We compute analytically the three-loop correlation function of the local operator tr ϕ3 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 tr ϕ2 case.