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N=8 Supergravity from Positivity.

John Joseph M Carrasco1, Alex Edison1, Nia Robles Del Pino1

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Summary
This summary is machine-generated.

The color-kinematic duality simplifies scattering amplitude calculations. A new algorithm, color-dual cut tiling, uses on-shell conditions to construct loop integrands, enabling nonplanar sector generation from planar cuts in supersymmetric gauge theory.

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Area of Science:

  • High Energy Physics
  • Quantum Field Theory
  • String Theory

Background:

  • The color-kinematic duality offers significant simplifications in constructing scattering amplitudes.
  • Bern-Carrasco-Johansson (BCJ) relations at tree-level are known to simplify amplitude calculations.

Purpose of the Study:

  • To demonstrate how satisfying tree-level BCJ relations can simplify loop computations, even if loop-level relations are not met.
  • To introduce a novel algorithm for constructing scattering integrands.
  • To show that planar cuts can generate nonplanar information in supersymmetric gauge theories.

Main Methods:

  • An agglomerative algorithm named "color-dual cut tiling" is introduced.
  • This algorithm builds the integrand from on-shell conditions applied to off-shell information.
  • The generalized double copy is utilized to relate gauge theory to gravity.

Main Results:

  • The color-dual cut tiling algorithm successfully generates the entire integrand from simple on-shell conditions.
  • For two-to-two scattering at three loops in maximally supersymmetric gauge theory, planar cuts (determined by positivity constraints) are sufficient to generate the nonplanar sector.
  • A representation of maximally supersymmetric gravity is generated as a functional of the planar SYM input.

Conclusions:

  • The developed algorithm significantly simplifies loop computations by leveraging color-kinematic duality.
  • The findings suggest a powerful method for constructing scattering amplitudes in quantum field theories.
  • The approach has potential for generalizations and applications in related areas of physics.