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Bootstrapping a Five-Loop Amplitude Using Steinmann Relations.

Simon Caron-Huot1,2, Lance J Dixon3,4, Andrew McLeod3

  • 1Niels Bohr International Academy & Discovery Center, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark.

Physical Review Letters
|December 24, 2016
PubMed
Summary
This summary is machine-generated.

Steinmann relations simplify scattering amplitude calculations in maximally supersymmetric Yang-Mills theory. This allows for the complete five-loop, six-particle amplitude determination using dual conformal symmetry and Regge exponentiation.

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Area of Science:

  • High Energy Physics
  • Quantum Field Theory
  • String Theory

Background:

  • Scattering amplitudes in quantum field theory possess a complex analytic structure.
  • Steinmann relations are crucial constraints on the discontinuities of these amplitudes.
  • Planar maximally supersymmetric Yang-Mills theory is a key model for studying non-perturbative effects.

Purpose of the Study:

  • To investigate the impact of Steinmann relations on scattering amplitude calculations.
  • To simplify the function space for bootstrap methods in specific quantum field theories.
  • To determine the complete five-loop, six-particle amplitude in planar maximally supersymmetric Yang-Mills theory.

Main Methods:

  • Applying Steinmann relations to constrain scattering amplitude discontinuities.
  • Utilizing dual conformal symmetry and Regge exponentiation as additional constraints.
  • Employing the hexagon function bootstrap method within the simplified function space.

Main Results:

  • Demonstrated that Steinmann relations significantly simplify the function space for hexagon bootstrap.
  • Successfully obtained the complete five-loop, six-particle amplitude.
  • The simplification enabled a more tractable calculation of the amplitude.

Conclusions:

  • Steinmann relations are powerful tools for simplifying complex amplitude calculations.
  • The methods employed provide a pathway to calculating higher-loop amplitudes.
  • This work advances the understanding of scattering amplitudes in supersymmetric Yang-Mills theory.