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The KLT Kernel in Twistor Space.

Tim Adamo1, Sonja Klisch1

  • 1School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh, EH9 3FD UK.

Communications in Mathematical Physics
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PubMed
Summary
This summary is machine-generated.

This study presents a novel double copy formulation for helicity-graded general relativity amplitudes using twistor space. It introduces a KLT-like integral kernel to unify gluon and graviton scattering, enabling new insights into theoretical physics.

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Area of Science:

  • Theoretical Physics
  • High Energy Physics
  • Mathematical Physics

Background:

  • The double copy relationship connects Yang-Mills theory and general relativity via the Kawai-Lewellen-Tye (KLT) momentum kernel.
  • Existing KLT formulations map gluon amplitudes to graviton amplitudes but lack a double copy for helicity-graded representations on twistor space.

Purpose of the Study:

  • To develop an explicit double copy representation for the tree-level, helicity-graded S-matrix of general relativity.
  • To utilize graph-theoretic methods and twistor space for this formulation.
  • To explore extensions and applications of the derived integral kernel.

Main Methods:

  • Employed graph-theoretic methods to derive a KLT-like integral kernel in twistor space.
  • Developed a method to glue two colour-ordered integrands for tree-level gluon scattering.
  • Utilized recursion relations to verify the inverted kernel's formula for biadjoint scalar theory.

Main Results:

  • Achieved an explicit double copy representation of the tree-level, helicity-graded S-matrix of general relativity.
  • Introduced a twistor space integral kernel that produces tree-level graviton amplitudes from gluon scattering integrands.
  • Derived a new formula for the tree-level S-matrix of biadjoint scalar theory by inverting the kernel.
  • Extended the integral kernel to graviton scattering in anti-de Sitter space and self-dual radiative spacetimes.

Conclusions:

  • The developed integral kernel provides a successful double copy formulation for helicity-graded general relativity.
  • This work bridges the gap in understanding double copy structures for twistor-based scattering amplitudes.
  • The findings offer potential for further exploration in quantum gravity and related theoretical frameworks.