Bootstrapping a Two-Loop Four-Point Form Factor

Abstract

We compute the two-loop four-point form factor of a length-3 half-BPS operator in planar N=4 SYM, which belongs to the class of two-loop five-point scattering observables with one off-shell color-singlet leg. A new bootstrapping strategy is developed to obtain this result by starting with an ansatz expanded in terms of master integrals and then solving the master coefficients via various physical constraints. We find that consistency conditions of infrared divergences and collinear limits, together with the cancellation of spurious poles, can fix a significant part of the ansatz. The remaining degrees of freedom can be fixed by one simple type of two-double unitarity cut. Full analytic results in terms of both symbol and Goncharov polylogarithms are provided.

11 pages, 3 figures, 4 tables; v2: references added, published version

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Cited by in corpus (12)

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• Two-Loop Hexa-Box Integrals for Non-Planar Five-Point One-Mass Processes
• Three-point energy correlator in $\mathcal{N}=4$ super Yang-Mills Theory
• Full-color three-loop three-point form factors in N=4 SYM
• Bootstrapping elliptic Feynman integrals using Schubert analysis
• Intersection theory rules symbology
• An Operator Product Expansion for Form Factors III. Finite Coupling and Multi-Particle Contributions
• A Two-Loop Four-Point Form Factor at Function Level
• Deciphering the Maximal Transcendentality Principle via Bootstrap
• All Two-Loop Feynman Integrals for Five-Point One-Mass Scattering
• Analytic two-Loop four-point form factor of the stress-tensor supermultiplet in $\mathcal{N}=4$ SYM
• Analytic Four-Point Lightlike Form Factors and OPE of Null-Wrapped Polygons