A functional renormalization group equation for foliated spacetimes

Abstract

We derive an exact functional renormalization group equation for the projectable version of Hořava-Lifshitz gravity. The flow equation encodes the gravitational degrees of freedom in terms of the lapse function, shift vector and spatial metric and is manifestly invariant under background foliation-preserving diffeomorphisms. Its relation to similar flow equations for gravity in the metric formalism is discussed in detail, and we argue that the space of action functionals, invariant under the full diffeomorphism group, forms a subspace of the latter invariant under renormalization group transformations. As a first application we study the RG flow of the Newton constant and the cosmological constant in the ADM formalism. In particular we show that the non-Gaussian fixed point found in the metric formulation is qualitatively unaffected by the change of variables and persists also for Lorentzian signature metrics.

44 pages, 3 figures

References in corpus (15)

• Exact evolution equation for the effective potential
• Membranes at Quantum Criticality
• Nonperturbative Quantum Gravity
• Ultraviolet properties of f(R)-Gravity
• Asymptotically Safe Lorentzian Gravity
• Taming perturbative divergences in asymptotically safe gravity
• Fixed points of quantum gravity in extra dimensions
• Bimetric Renormalization Group Flows in Quantum Einstein Gravity
• Matter Induced Bimetric Actions for Gravity
• On the Renormalizability of Horava-Lifshitz-type Gravities
• The Universal RG Machine
• General Covariance in Gravity at a Lifshitz Point
• Non-perturbative thermal flows and resummations
• Fixed points of quantum gravity in higher dimensions
• On the true nature of renormalizability in Horava-Lifshitz gravity

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