Extracting Einstein from the loop-level double-copy

Abstract

The naive double-copy of (multi) loop amplitudes involving massive matter coupled to gauge theories will generically produce amplitudes in a gravitational theory that contains additional contributions from propagating antisymmetric tensor and dilaton states even at tree-level. We present a graph-based approach that combines the method of maximal cuts with double-copy construction to offer a systematic framework to isolate the pure Einstein-Hilbert gravitational contributions through loop level. Indeed this allows for a bootstrap of pure-gravitational results from the double-copy of massive scalar-QCD. We apply this to construct the novel result of the D-dimensional one-loop five-point QFT integrand relevant in the classical limit to generating observables associated with the radiative effects of massive black-hole scattering via pure Einstein-Hilbert gravity.

Reconstructing Classical Spacetimes from the S-Matrix in Twistor Space

“…In fact, [78,79] have argued that the Kerr-Schild double copy structure [101,102,[110][111][112][113][114][115][116][117] follows from the Penrose transform. Due to this, it can be readily checked that our formula (13) links the KS double copy directly to the double copy between gauge and gravity massive amplitudes of [46], also developed in [47,105,106,[118][119][120][121][122][123][124][125][126][127].…”

“…the generation of gravitational waves. The associated amplitudes may have more matter sources but only one outgoing graviton [6,47,51,105,106], making them suitable for the techniques presented (see [34] for a recent discussion of retarded vs Feynman propagators in this context). They are controlled to some extent by soft factorization [46]: Indeed the amplitude M 3 treated here is the simplest instance of such, where the Coulomb poles of the soft factor 1 u•k±i are equivalent to the delta function δ(u • k).…”

The SAGEX Review on Scattering Amplitudes, Chapter 14: Classical Gravity from Scattering Amplitudes

“…We included a factor −1/16 which arises in the double copy [5,13]. For the pure gravitational theory, in this example, the double copy would require a more involved procedure to project out the dilaton [93]. Accordingly, the impulse in the gravitodilatonic scattering of two massive particles is, ∆p µ,(0) 1…”

“…Another interesting observable which connects to five-point amplitudes is the radiated angular momentum [26]. The relevance of five-point amplitudes with massive legs to gravitational radiation motivates determining these amplitudes at loop order [93,118].…”

Off-Shell Color-Kinematics Duality for Chern-Simons

“…For tree-level amplitudes in purely-adjoint gauge theories, the application of the double copy is equivalent to the field-theory limit of the Kawai-Lewellen-Tye (KLT) relations [73] between open and closed string amplitudes. The double-copy applies to a large web of gravitational theories [2,40,[74][75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90][91][92][93], including string theory [94][95][96][97][98][99][100] and ambi-twistor string constructions [101][102][103][104][105][106]. The double copy has been extended to classical solutions in general relativity, such as Schwarzschild and Kerr black holes and calculations relevant to gravitational-wave physics [132][133][134][135][136][137][138][139][140][141]…”