Gravity as the square of gauge theory

          @misc{ pirsa_PIRSA:21030011,
            doi = {10.48660/21030011},
            url = {https://pirsa.org/21030011},
            author = {Borsten, Leron},
            keywords = {Mathematical physics, Particle Physics, Quantum Fields and Strings},
            language = {en},
            title = {Gravity as the square of gauge theory},
            publisher = {Perimeter Institute},
            year = {2021},
            month = {mar},
            note = {PIRSA:21030011 see, \url{https://pirsa.org}}
          }
          

Abstract

Can gravity, in certain regards, be the `product' of two gauge theories, such as those appearing in the Standard Model? I will begin by reviewing the Bern—Carrasco—Johansson colour—kinematics duality conjecture, which implies that one can write the scattering amplitudes of Einstein-Hilbert gravity (coupled to a Kalb-Ramond 2-form and dilaton scalar) as the double copy of Yang—Mills amplitudes. Although the colour—kinematics duality, and therefore the double copy, was quickly established at the tree level, it remains a longstanding open problem at the loop level, despite highly non-trivial explicit examples. I will then describe how one can take this `gravity = gauge x gauge' amplitude paradigm `off-shell’ as a product of spacetime fields: the Yang-Mills BRST-Lagrangian itself double copies into perturbatively quantised Einstein-Hilbert gravity coupled to a Kalb-Ramond 2-form and dilaton, establishing the validity of the double copy to all orders, tree and loop. I will end by briefly discussing the homotopy algebras underpinning this result and the inclusion of supersymmetry, which reveals fascinating octonionic structures (some very well-known, others completely new) that will be the subject of Mia Hughes's talk in the following week.