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Master integrals for the four-loop Sudakov form factor. (English) Zbl 1332.81126
Summary: The light-like cusp anomalous dimension is a universal function in the analysis of infrared divergences. In maximally (\(\mathcal{N} = 4\)) supersymmetric Yang-Mills theory (SYM) in the planar limit, it is known, in principle, to all loop orders. The non-planar corrections are not known in any theory, with the first appearing at the four-loop order. The simplest quantity which contains this correction is the four-loop two-point form factor of the stress tensor multiplet. This form factor was largely obtained in integrand form in a previous work for \(\mathcal{N} = 4\) SYM, up to a free parameter. In this work, a reduction of the appearing integrals obtained by solving integration-by-parts (IBP) identities using a modified version of is reported. The form factor is shown to be independent of the remaining parameter at integrand level due to an intricate pattern of cancellations after IBP reduction. Moreover, two of the integral topologies vanish after reduction. The appearing master integrals are cross-checked using independent algebraic-geometry techniques explored in the package. The latter results provide the basis of master integrals applicable to generic form factors, including those in Quantum Chromodynamics. Discrepancies between explicitly solving the IBP relations and the MINT approach are highlighted. Remaining bottlenecks to completing the computation of the four-loop non-planar cusp anomalous dimension in \(\mathcal{N} = 4\) SYM and beyond are identified.

MSC:
81T13 Yang-Mills and other gauge theories in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
81T18 Feynman diagrams
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
81-08 Computational methods for problems pertaining to quantum theory
14C35 Applications of methods of algebraic \(K\)-theory in algebraic geometry
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