Manifestly diffeomorphism invariant classical Exact Renormalization Group

TL;DR

This paper develops a diffeomorphism invariant Wilsonian Renormalization Group approach for classical gravity, enabling calculations without gauge fixing or background dependence, and lays groundwork for quantum gravity.

Contribution

It introduces a manifestly diffeomorphism invariant RG framework for classical gravity and explores fixed points, paving the way for a quantum gravity formulation.

Findings

Effective action computed without gauge fixing

Equivalence of background-independent and background-dependent results

Formulation of flow equations for fixed points

Abstract

We construct a manifestly diffeomorphism invariant Wilsonian (Exact) Renormalization Group for classical gravity, and begin the construction for quantum gravity. We demonstrate that the effective action can be computed without gauge fixing the diffeomorphism invariance, and also without introducing a background space-time. We compute classical contributions both within a background-independent framework and by perturbing around a fixed background, and verify that the results are equivalent. We derive the exact Ward identities for actions and kernels and verify consistency. We formulate two forms of the flow equation corresponding to the two choices of classical fixed-point: the Gaussian fixed point, and the scale invariant interacting fixed point using curvature-squared terms. We suggest how this programme may completed to a fully quantum construction.