Abstract
We compute the renormalization group running of the Newton constant and the parameter $\ensuremath{\lambda}$ in ($3+1$)-dimensional projectable Ho\ifmmode \check{r}\else \v{r}\fi{}ava gravity. We use the background-field method, expanding around configurations with flat spatial metric, but nonvanishing shift. This allows us to reduce the number of interaction vertices and thereby drastically simplify the calculations. The gauge-invariant $\ensuremath{\beta}$-function of $\ensuremath{\lambda}$ has two families of zeros, attractive in the infrared and ultraviolet, respectively. They are candidates for the fixed points of the full renormalization group flow of the theory, once the $\ensuremath{\beta}$-functions for the rest of the couplings are added.
Highlights
Since the formulation of general relativity (GR) a century ago and of quantum mechanics a few years later, the quest for a theory unifying the two—quantum gravity (QG)—has been one of the biggest endeavors in theoretical physics
We compute the renormalization group running of the Newton constant and the parameter λ in (3 þ 1)dimensional projectable Horava gravity
While other known fundamental interactions are successfully described within the formalism of local perturbative quantum field theory (QFT), most approaches to QG involve departures from this framework
Summary
Since the formulation of general relativity (GR) a century ago and of quantum mechanics a few years later, the quest for a theory unifying the two—quantum gravity (QG)—has been one of the biggest endeavors in theoretical physics. A simple way out of this problem in four spacetime dimensions is to extend the gravitational Lagrangian with terms quadratic in curvature [4,5,6] so that UV divergences are softened by higher powers of four-momenta in the propagators This theory is thereby renormalizable and even asymptotically free for some regions of the parameter space, unitarity is jeopardized by the presence of four time derivatives in the action, which gives rise to a propagating Ostrogradsky ghost with negative norm in the Hilbert space [7,8].
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