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 ???$$\hbox {gravity} = \hbox {gauge} \times \hbox {gauge}$$???. This is followed by modern approaches to gauge/gravity scattering amplitude relations, focussing on the Bern???Carrasco???Johansson colour-kinematic 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 ???$$\hbox {gravity} =\hbox {gauge} \times \hbox {gauge}$$???. 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 ???$$\hbox {gravity} =\hbox {gauge} \times \hbox {gauge}$$???. This framework centres on a convolutive product of gauge theories, at the level of spacetime fields themselves, that yields gravitational theories.