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

References in corpus (7)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Bootstrapping an NMHV amplitude through three loops
• BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
• Adjoint BFKL at finite coupling: a short-cut from the collinear limit
• Evaluating the 6-point Remainder Function Near the Collinear Limit

Cited by in corpus (10)

• A Periodic Table of Effective Field Theories
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• Bootstrapping the QCD soft anomalous dimension
• Elliptic polylogarithms and Feynman parameter integrals
• The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity
• Multi-Loop Positivity of the Planar $\mathcal{N}=4$ SYM Six-Point Amplitude
• Analytic all-plus-helicity gluon amplitudes in QCD
• Manifestly Dual-Conformal Loop Integration
• The Sklyanin Bracket and Cluster Adjacency at All Multiplicity
• Regge meets collinear in strongly-coupled $\mathcal{N}=4$ super Yang-Mills