Differential operators built from the 1-loop CHY formula map the gravitational 1-loop Feynman integrand to those of Einstein-Yang-Mills, pure Yang-Mills, Born-Infeld, bi-adjoint scalar, and other theories, with factorization into tree-level operators under unitarity cuts.
Gravity as the Square of Gauge Theory
7 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We explore consequences of the recently discovered duality between color and kinematics, which states that kinematic numerators in a diagrammatic expansion of gauge-theory amplitudes can be arranged to satisfy Jacobi-like identities in one-to-one correspondence to the associated color factors. Using on-shell recursion relations, we give a field-theory proof showing that the duality implies that diagrammatic numerators in gravity are just the product of two corresponding gauge-theory numerators, as previously conjectured. These squaring relations express gravity amplitudes in terms of gauge-theory ingredients, and are a recasting of the Kawai, Lewellen and Tye relations. Assuming that numerators of loop amplitudes can be arranged to satisfy the duality, our tree-level proof immediately carries over to loop level via the unitarity method. We then present a Yang-Mills Lagrangian whose diagrams through five points manifestly satisfy the duality between color and kinematics. The existence of such Lagrangians suggests that the duality also extends to loop amplitudes, as confirmed at two and three loops in a concurrent paper. By "squaring" the novel Yang-Mills Lagrangian we immediately obtain its gravity counterpart. We outline the general structure of these Lagrangians for higher points. We also write down various new representations of gauge-theory and gravity amplitudes that follow from the duality between color and kinematics.
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The Kerr-Schild and twistorial double copies are equivalent for self-dual vacuum Kerr-Schild spacetimes.
Bogoliubov coefficients from scattering a scalar in a collapsing EM background (single copy of Vaidya) match ray-tracing results and connect to Hawking radiation through the double copy.
A recursive construction expands tree YM amplitudes to YMS and BAS amplitudes from soft theorems while preserving gauge invariance at each step.
New differential operators transmute 1-loop gravitational integrands to Yang-Mills ones and enable a unified web of expansions relating integrands of gravity, gauge, scalar and effective theories.
The Kerr-Schild double copy does not map residual symmetries between Yang-Mills and gravity; gravitational conformal Killing vectors are shown to be BRST-exact after a Weyl-compensated complex, leaving only global isometries.
The regularization prescription for the Weyl double copy restores consistency with the Kerr-Schild double copy across three distinct Lifshitz black hole examples.
citing papers explorer
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On differential operators and unifying relations for $1$-loop Feynman integrands
Differential operators built from the 1-loop CHY formula map the gravitational 1-loop Feynman integrand to those of Einstein-Yang-Mills, pure Yang-Mills, Born-Infeld, bi-adjoint scalar, and other theories, with factorization into tree-level operators under unitarity cuts.
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The Penrose Transform and the Kerr-Schild double copy
The Kerr-Schild and twistorial double copies are equivalent for self-dual vacuum Kerr-Schild spacetimes.
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Hawking Radiation meets the Double Copy
Bogoliubov coefficients from scattering a scalar in a collapsing EM background (single copy of Vaidya) match ray-tracing results and connect to Hawking radiation through the double copy.
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Recursive construction for expansions of tree Yang-Mills amplitudes from soft theorem
A recursive construction expands tree YM amplitudes to YMS and BAS amplitudes from soft theorems while preserving gauge invariance at each step.
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Transmutation operators and expansions for $1$-loop Feynman integrands
New differential operators transmute 1-loop gravitational integrands to Yang-Mills ones and enable a unified web of expansions relating integrands of gravity, gauge, scalar and effective theories.
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Residual Symmetries and Their Algebras in the Kerr-Schild Double Copy
The Kerr-Schild double copy does not map residual symmetries between Yang-Mills and gravity; gravitational conformal Killing vectors are shown to be BRST-exact after a Weyl-compensated complex, leaving only global isometries.
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Weyl double copy in Lifshitz spacetimes
The regularization prescription for the Weyl double copy restores consistency with the Kerr-Schild double copy across three distinct Lifshitz black hole examples.