Abstract
It is well known in quantum field theory that the off-shell effective action depends on the gauge choice and field parametrization used in calculating it. Nevertheless, the typical scheme in which the scenario of asymptotically safe gravity is investigated is an off-shell version of the functional renormalization group equation. Working with the Einstein–Hilbert truncation as a test bed, we develop a new scheme for the analysis of asymptotically safe gravity in which the on-shell part of the effective action is singled out and we show that the beta function for the essential coupling has no explicit gauge dependence. In order to reach our goal, we introduce several technical novelties, including a different decomposition of the metric fluctuations, a new implementation of the ghost sector and a new cut-off scheme. We find a nontrivial fixed point, with a value of the cosmological constant that is independent of the gauge-fixing parameters.
Highlights
The renormalization group is a powerful framework for the understanding of fundamental issues in quantum field theory and its relation to critical phenomena
The general framework of such methods is centered around an exact functional renormalization group equation (FRGE) for the scale-dependent quantum effective action, called effective average action (EAA)
The main approximation scheme in the quest for non-trivial fixed points is that of truncating the theory space, by which we mean specifying an ansatz for the EAA and discarding any term in the FRGE that would lead the flow out of the ansatz
Summary
The renormalization group is a powerful framework for the understanding of fundamental issues in quantum field theory and its relation to critical phenomena. A proper Faddeev-Popov procedure (or BRST symmetry) ensures exactly such independence for the physical observables This is not the case for the effective action, which is not an observable per se, and in particular its renormalization group running depends on the gauge-fixing choice. If the variation contains a part proportional to the equations of motion, ∂kΓk ∼ X · δΓk/δΦ + ..., we can compensate it with a field redefinition Φ → Φ+δkX In this sense certain components of the flow are said to be redundant or inessential. The present work is motivated by the desire to isolate the on-shell component of the RG flow of gravity, which we would expect to be gauge- and parametrization-independent.
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