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We found that double-copy maps in effective field theory are constrained by self-consistency. The resulting kernel interpolates between string theory and field theory relations, with no other possibilities.

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Area of Science:

  • Theoretical Physics
  • Quantum Field Theory
  • String Theory

Background:

  • The double-copy prescription relates gauge theories to gravity.
  • Effective field theories (EFTs) provide a framework for describing physical phenomena at specific energy scales.
  • Understanding constraints on double-copy maps is crucial for unifying these theoretical frameworks.

Purpose of the Study:

  • To investigate the constraints on double-copy maps for amplitudes in effective field theory.
  • To determine the structure of the double-copy kernel and its dependence on kinematic variables.
  • To clarify the relationship between string theory and field theory relations in the context of double copies.

Main Methods:

  • Analyzing self-consistency and locality conditions for four-point amplitudes in effective field theory.
  • Deriving the general form of the double-copy kernel.
  • Comparing the derived kernel with existing double-copy constructions like Kawai-Lewellen-Tye (KLT) and period integrals.

Main Results:

  • Double-copy maps are severely constrained by self-consistency (four points) and locality (six points).
  • The derived double-copy kernel depends on two parameters and a symmetric function of s, t, u.
  • The kernel interpolates between the KLT string double copy and open/closed string period integrals.
  • Amplitudes must satisfy either string monodromy relations or field theory Kleiss-Kuijf (KK) and Bern, Carrasco, and Johansson (BCJ) relations.

Conclusions:

  • The study elucidates the single-valued projection property of Riemann zeta-function values for four-point string theory double copies.
  • The findings establish a unique set of possible relations that double-copied amplitudes must obey.
  • This work provides a deeper understanding of the connections between string theory and quantum field theory through the double-copy mechanism.