Bootstrapping a Five-Loop Amplitude Using Steinmann Relations

Simon Caron-Huot, Lance J. Dixon, Andrew McLeod, and Matt von Hippel

Phys. Rev. Lett. 117, 241601 – Published 5 December 2016

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.

Received 9 September 2016

DOI:https://doi.org/10.1103/PhysRevLett.117.241601

Physics Subject Headings (PhySH)

Gauge theories Large-N expansion in field theory Non-Abelian gauge theories Perturbation theory Quantum field theory Scattering amplitudes

Supersymmetry

Particles & Fields

Authors & Affiliations

Simon Caron-Huot^1,2, Lance J. Dixon^3,4, Andrew McLeod³, and Matt von Hippel⁵

¹Niels Bohr International Academy & Discovery Center, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
²Department of Physics, McGill University, 3600 Rue University, Montréal, Québec, Canada H3A 2T8
³SLAC National Accelerator Laboratory, Stanford University, Stanford, California 94309, USA
⁴Kavli Institute for Theoretical Physics, UC Santa Barbara, Santa Barbara, California 93106, USA
⁵Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada