Gravity as the square of gauge theory: a review

Abstract

We briefly review the manifold incarnations and facets of the notion that gravity, in certain regards, can be re-conceived as the product of two gauge theories. We begin with a short history of the relationship between gauge and gravity theories in the context of "gravity = gauge × gauge". This is followed by modern approaches to gauge/gravity scattering amplitude relations, focussing on the Bern-Carrasco-Johansson colourkinematic duality and double-copy construction of gravitational amplitudes from gauge amplitudes. This includes a partial characterisation of what gravity theories admit a gauge theory squared origin. We then consider classical and off-shell perspectives on "gravity = gauge × gauge". First we review field theoretic approaches to understanding the colour-kinematic duality and the double-copy prescription, including kinematic algebras and colour-kinematic duality and double-copy manifesting Lagrangians. We then consider classical double-copy-like methods for constructing gravitational solutions from gauge theory solutions. To close, we consider a purely field theoretic take on "gravity = gauge × gauge". This framework centres on a convolutive product of gauge theories, at the level of spacetime fields themselves, that yields gravitational theories.

The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order

“…This has yielded both pragmatic applications, particularly in the context of gravity-wave astronomy, as well as emphasising interesting questions and features of the double-copy itself. For a review of these ideas, including the many topics not mentioned here, their applications and further references see [100][101][102].…”

“…One of the main advantages of the BRST formulation of the field theory convolution product is that it gives an elegant solution to the issue of the mixing of the dilaton and JHEP07(2020)093 graviton degrees of freedom pointed out in e.g. [6,74], as detailed in [2,72,102,105]. 1 In particular, the BRST approach opens the door to an off-shell construction for pure Einstein-Hilbert gravity.…”

The classical double copy of a point charge

“…Generically, the expected setting for the classical double copy is perturbative. This is how most discussions of the double copy for classical solutions have proceeded: the first approaches [35][36][37], constructions based on the local symmetries [33,[38][39][40][41][42], use of the worldline formalism [32,[43][44][45][46][47][48][49][50][51][52], and perturbation theory on curved backgrounds [53,54]. A double copy for classical observables (rather than solutions to the equations of motion) that follows more directly from that of scattering amplitudes has been explored with a view to gravitational phenomenology [55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71], a subject of obvious interest following the discovery of gravitational waves.…”

Dark Side of Weyl Gravity

“…Namely, such theories have dimensionful couplings and hence they are perturbatively non-renormalizable when quantized. More recently, the deep relationship between gauge and gravity theories has further been explored in the light of the holographic principle (as realized, for example, by the AdS/CFT correspondence [6]) and the "gravity = gauge × gauge" principle (as embodied, for example, in the Ben-Carrasco-Johansson color-kinematic correspondence [7]).…”