Abstract
We discuss a variation of quadratic gravity in which the gravitational interaction remains weakly coupled at all energies, but is assisted by a Yang-Mills gauge theory which becomes strong at the Planck scale. The Yang-Mills interaction is used to induce the usual Einstein-Hilbert term, which was taken to be small or absent in the original action. We study the spin-two propagator in detail, with a focus on the high mass resonance which is shifted off the real axis by the coupling to real decay channels. We calculate scattering in the $J=2$ partial wave and show explicitly that unitarity is satisfied. The theory will in general have a large cosmological constant and we study possible solutions to this, including a unimodular version of the theory. Overall, the theory satisfies our present tests for being a ultraviolet completion of quantum gravity.
Highlights
There are many exotic approaches to quantum gravity, but comparatively little present work exploring the option of describing gravity by a renormalizable quantum field theory (QFT)
There are two main topics connected to other terms in the action, (1) the cosmological constant and (2) the R2 term in the quadratic action which is associated with the scalar d.o.f. in quadratic gravity
There are several features of this theory which differ from usual expectation
Summary
There are many exotic approaches to quantum gravity, but comparatively little present work exploring the option of describing gravity by a renormalizable quantum field theory (QFT). Nature has shown that the other fundamental interactions, i.e. those of the standard model, are described by renormalizable QFTs at present energies, so this should be the most conservative approach. The key question is to determine if any renormalizable QFT can serve as a UV completion for gravity. We explore such a variation which we feel is well suited for being a controlled approach using present techniques, with encouraging results. The distinctive feature of a renormalizable QFT treatment of gravity is simple to diagnose.
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