Gravity-induced emergence of the Fermi scale in quantum quadratic gravity

Abstract: In the framework of asymptotic safety, we study quantum quadratic gravity in the presence of the Higgs field considered as non-separable from the vacuum. The theory flows to a high energy fixed point where the Higgs field is strongly coupled to gravity, its potential is symmetric, and the quadratic Weyl curvature coupling is large. The latter renders the ghost graviton an unstable high mass resonance which renders unitarity in the spirit of Lee-Week type theories. Furthermore, if the scalar graviton is tachyonic then there will be a low energy fixed point where tachyonic condensation leads to a new stable vacuum. At this fixed point the symmetry breaks and the Fermi scale emerges, and the behavior of the Higgs field is classical (not influenced by gravitational interaction). Gravity at the UV scale is purely quadratic whereas at the Fermi scale it is linear, and in the intermediate region both contributions are relevant. Thus, at the Fermi scale the quadratic curvature fields disappear through the ghost instability and tachyon condensation, giving rise to Einstein gravity and the electroweak phase transition.