Noncommutative twisted de Rham theory derives the intersection number of open-string contours whose inverse is the double-copy kernel for four-point AdS string generating functions.
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Perturbative Quantum Gravity as a Double Copy of Gauge Theory
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abstract
In a previous paper we observed that (classical) tree-level gauge theory amplitudes can be rearranged to display a duality between color and kinematics. Once this is imposed, gravity amplitudes are obtained using two copies of gauge-theory diagram numerators. Here we conjecture that this duality persists to all quantum loop orders and can thus be used to obtain multiloop gravity amplitudes easily from gauge-theory ones. As a nontrivial test, we show that the three-loop four-point amplitude of N = 4 super-Yang-Mills theory can be arranged into a form satisfying the duality, and by taking double copies of the diagram numerators we obtain the corresponding amplitude of N = 8 supergravity. We also remark on a non-supersymmetric two-loop test based on pure Yang-Mills theory resulting in gravity coupled to an anti-symmetric tensor and dilaton.
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Establishes the Topological Graviton Equivalence Theorem to prove large energy cancellations in N-point massive graviton amplitudes and constructs three- and four-point amplitudes via double copy from topologically massive Yang-Mills.
A modular assembly method constructs D-dimensional higher-derivative four-point amplitudes involving fermions from gauge-invariant blocks, color factors, and permutation-invariant scalar polynomials.
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.
Trapped black hole interiors admit exact time-dependent classical double copy via Kantowski-Sachs patches from static Kerr-Schild data, characterized by p_parallel = -ρ, with finite single-copy fields in regular solutions like Bardeen.
A single complex optical seed built from expansion and twist organizes stationary Kerr-Schild geometries, reconstructs the congruence, and encodes the zeroth-copy data that generates both the gravitational profile and the single-copy gauge field.
The Smarr formula is structurally identical to the single-copy Gauss's law for Kerr-Schild black holes, with the AdS pressure-volume term arising from gauge background subtraction.
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.
Hidden zeros extend to higher-derivative tree-level gluon and graviton amplitudes, with systematic cancellation of propagator singularities shown via bi-adjoint scalar expansions.
A recursion formula for ℓ-loop planar integrands in colored QFTs is derived from the classical equation of motion via comb components and loop kernels.
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.
All self-dual theories with or without higher-spin fields possess nontrivial tree-level amplitudes in Kleinian or complex Minkowski kinematics, completing the celestial analogue of the higher-spin duality.
Black hole response theory in WQFT exactly reproduces the Aichelburg-Sexl shockwave metric, geodesics, and the transfer matrix for gravitational-wave scattering off it via post-Minkowskian resummation.
A new Mathematica package computes tree amplitudes with arbitrary gauge bosons and arbitrarily charged massless fermions by reducing distinct-flavor partial amplitudes to linear combinations of single-flavor supersymmetric Yang-Mills components.
Kerr-Schild double copy of the RS II black string produces a sourceless Maxwell single copy and a warp-induced massive scalar zeroth copy, with an alternative splitting giving inequivalent gauge and scalar fields.
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.
Hidden zeros in NLSM amplitudes are proven via modified BCFW recursion, with 2-split holding only under careful current definition.
Hidden zeros in tree-level amplitudes of several theories are attributed to zeros of bi-adjoint scalar amplitudes via universal expansions, with a mechanism shown to cancel potential propagator divergences in gravity.
citing papers explorer
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Twisted de Rham theory for string double copy in AdS
Noncommutative twisted de Rham theory derives the intersection number of open-string contours whose inverse is the double-copy kernel for four-point AdS string generating functions.
-
Structure of Chern-Simons Graviton Scattering Amplitudes from Topological Graviton Equivalence Theorem and Double Copy
Establishes the Topological Graviton Equivalence Theorem to prove large energy cancellations in N-point massive graviton amplitudes and constructs three- and four-point amplitudes via double copy from topologically massive Yang-Mills.
-
$D$-Dimensional Modular Assembly of Higher-Derivative Four-Point Contact Amplitudes Involving Fermions
A modular assembly method constructs D-dimensional higher-derivative four-point amplitudes involving fermions from gauge-invariant blocks, color factors, and permutation-invariant scalar polynomials.
-
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.
-
Black Hole Interiors as a Laboratory for Time-Dependent Classical Double Copy
Trapped black hole interiors admit exact time-dependent classical double copy via Kantowski-Sachs patches from static Kerr-Schild data, characterized by p_parallel = -ρ, with finite single-copy fields in regular solutions like Bardeen.
-
Untwisting the double copy: the zeroth copy as an optical seed
A single complex optical seed built from expansion and twist organizes stationary Kerr-Schild geometries, reconstructs the congruence, and encodes the zeroth-copy data that generates both the gravitational profile and the single-copy gauge field.
-
The Smarr Formula is Gauss's Law: A Kerr-Schild Single-Copy Perspective
The Smarr formula is structurally identical to the single-copy Gauss's law for Kerr-Schild black holes, with the AdS pressure-volume term arising from gauge background subtraction.
-
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.
-
Hidden zeros for higher-derivative YM and GR amplitudes at tree-level
Hidden zeros extend to higher-derivative tree-level gluon and graviton amplitudes, with systematic cancellation of propagator singularities shown via bi-adjoint scalar expansions.
-
Systematic approach to $\ell$-loop planar integrands from the classical equation of motion
A recursion formula for ℓ-loop planar integrands in colored QFTs is derived from the classical equation of motion via comb components and loop kernels.
-
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.
-
Amplitudes in self-dual (higher-spin) theories
All self-dual theories with or without higher-spin fields possess nontrivial tree-level amplitudes in Kleinian or complex Minkowski kinematics, completing the celestial analogue of the higher-spin duality.
-
Black Hole Response Theory and its Exact Shockwave Limit
Black hole response theory in WQFT exactly reproduces the Aichelburg-Sexl shockwave metric, geodesics, and the transfer matrix for gravitational-wave scattering off it via post-Minkowskian resummation.
-
Tree Amplitudes with Charged Matter in Pure Gauge Theory
A new Mathematica package computes tree amplitudes with arbitrary gauge bosons and arbitrarily charged massless fermions by reducing distinct-flavor partial amplitudes to linear combinations of single-flavor supersymmetric Yang-Mills components.
-
Kerr-Schild Double Copy of the Randall-Sundrum Black String
Kerr-Schild double copy of the RS II black string produces a sourceless Maxwell single copy and a warp-induced massive scalar zeroth copy, with an alternative splitting giving inequivalent gauge and scalar fields.
-
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.
-
Hidden Zeros and $2$-split via BCFW Recursion Relation
Hidden zeros in NLSM amplitudes are proven via modified BCFW recursion, with 2-split holding only under careful current definition.
-
Note on hidden zeros and expansions of tree-level amplitudes
Hidden zeros in tree-level amplitudes of several theories are attributed to zeros of bi-adjoint scalar amplitudes via universal expansions, with a mechanism shown to cancel potential propagator divergences in gravity.