Effective action of dilaton gravity as the classical double copy of Yang-Mills theory

Abstract

We compute the classical effective action of color charges moving along worldlines by integrating out the Yang-Mills gauge field to next-to-leading order in the coupling. An adapted version of the Bern-Carrasco-Johansson (BCJ) double-copy construction known from quantum scattering amplitudes is then applied to the Feynman integrands, yielding the prediction for the classical effective action of point masses in dilaton gravity. We check the validity of the result by independently constructing the effective action in dilaton gravity employing field redefinitions and gauge choices that greatly simplify the perturbative construction. Complete agreement is found at next-to-leading order. Finally, upon performing the post-Newtonian expansion of our result, we find agreement with the corresponding action of scalar-tensor theories known from the literature. Our results represent a proof of concept for the classical double-copy construction of the gravitational effective action and provides another application of a BCJ-like double copy beyond scattering amplitudes.

Double copy of massive scalar QCD

“…This connection comes about from an effective field theory perspective where spinless blackholes may be modeled by massive scalar particles in the classical and large mass limit (for introductory reviews see [41][42][43]). While the double copy procedure could be efficiently applied up to the 1PN and 2PM level [18,[20][21][22][23][24]26] a recent double-copy construction at the 2PN and 3PM level of the present authors and Steinhoff revealed a disagreement with the known 2PN result in dilatongravity [44].…”

Breakdown of the classical double copy for the effective action of dilaton-gravity at NNLO

“…Unfortunately, we have to report that the effective action generated by the proposed double-copy procedure of [57] fails to agree with the desired dilaton-gravity result at this next-to-next-to leading order. The dilaton-gravity potential at 2PN we seeked to reproduce is available in the literature [59] and we have also checked its static contributions from a probe limit comparing to the Janis-Newman-Winicour (JNW) naked singularity [60] as well as through a direct Feynman diagramatic computation in order to be certain of the discrepancy.…”

Observables and amplitudes for spinning particles and black holes

“…While only proven at tree-level for pure gauge theory [60], this conjecture can be applied to both massless and massive states [61,62] and has a wealth of non-trivial supporting evidence [63][64][65]. It raises the provocative question of whether exact solutions in general relativity satisfy similar simple relationships to their classical Yang-Mills counterparts, coined the classical double copy [66][67][68][69][70][71][72][73][74][75][76][77][78][79][80]. Such a relationship has indeed been found in the gravitational radiation emitted by spinning sources at 1PM order [81,82].…”