Bootstrapping a Five-Loop Amplitude Using Steinmann Relations

Abstract

The analytic structure of scattering amplitudes is restricted by Steinmann relations, which enforce the vanishing of certain discontinuities of discontinuities. We show that these relations dramatically simplify the function space for the hexagon function bootstrap in planar maximally supersymmetric Yang-Mills theory. Armed with this simplification, along with the constraints of dual conformal symmetry and Regge exponentiation, we obtain the complete five-loop six-particle amplitude.

5 pages, 2 figures, 1 impressive table, and 2 ancillary files. v2: a few clarifications and references added; version to appear in PRL

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• All-order amplitudes at any multiplicity in the multi-Regge limit
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• Dual Conformal Structure Beyond the Planar Limit
• Analytic Two-Loop Higgs Amplitudes in Effective Field Theory and the Maximal Transcendentality Principle
• Boundaries of Amplituhedra and NMHV Symbol Alphabets at Two Loops
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• The Principle of Maximal Transcendentality and the Four-Loop Collinear Anomalous Dimension
• Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
• Notes on cluster algebras and some all-loop Feynman integrals
• The symbol and alphabet of two-loop NMHV amplitudes from $\bar{Q}$ equations
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• Loop-tree duality from vertices and edges
• Tropical fans, scattering equations and amplitudes
• Multi-Regge Limit of the Two-Loop Five-Point Amplitudes in $\mathcal{N}=4$ Super Yang-Mills and $\mathcal{N}=8$ Supergravity
• Truncated cluster algebras and Feynman integrals with algebraic letters
• The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
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