Universality and symmetry breaking in conformally reduced quantum gravity

Abstract:We use the Wetterich-equation to study the renormalization group flow of f (R)-gravity in a three-dimensional, conformally reduced setting. Building on the exact heat kernel for maximally symmetric spaces, we obtain a partial differential equation which captures the scale-dependence of f (R) for positive and, for the first time, negative scalar curvature. The effects of different background topologies are studied in detail and it is shown that they affect the gravitational RG flow in a way that is not visible in finite-dimensional truncations. Thus, while featuring local background independence, the functional renormalization group equation is sensitive to the topological properties of the background. The detailed analytical and numerical analysis of the partial differential equation reveals two globally well-defined fixed functionals with at most a finite number of relevant deformations. Their properties are remarkably similar to two of the fixed points identified within the R 2 -truncation of full Quantum Einstein Gravity. As a byproduct, we obtain a nice illustration of how the functional renormalization group realizes the "integrating out" of fluctuation modes on the three-sphere.

Section: Jhep06(2014)026mentioning

confidence: 99%

RG flows of Quantum Einstein Gravity on maximally symmetric spaces

Demmel

Saueressig

Zanusso

2014

“…Note that as far as the effective action is concerned, this sign can be accommodated in a natural way as already discussed in [7], although see also ref. [33] and our comments in section 7.1. In the context of conformally reduced quantum gravity it has also been discussed in [15,16,18].…”

Section: Derivative Expansion Of the Effective Actionmentioning

confidence: 99%

“…[32] where these conditions indeed hold, or f (φ) = φ 2 , e.g. [18,33] where to avoid double counting, arguablyφ ought to be restricted to be positive (without loss of generality).…”

Section: Jhep04(2015)118mentioning

confidence: 99%

Background independent exact renormalization group for conformally reduced gravity

Dietz

Morris

2015

126

Within the conformally reduced gravity model, where the metric is parametrised by a function f (φ) of the conformal factor φ, we keep dependence on both the background and fluctuation fields, to local potential approximation and O(∂ 2 ) respectively, making no other approximation. Explicit appearances of the background metric are then dictated by realising a remnant diffeomorphism invariance. The standard non-perturbative Renormalization Group (RG) scale k is inherently background dependent, which we show in general forbids the existence of RG fixed points with respect to k. By utilising transformations that follow from combining the flow equations with the modified split Ward identity, we uncover a unique background independent notion of RG scale,k. The corresponding RG flow equations are then not only explicitly background independent along the entire RG flow but also explicitly independent of the form of f . In general f (φ) is forced to be scale dependent and needs to be renormalised, but if this is avoided then k-fixed points are allowed and furthermore they coincide withk-fixed points.

“…Therefore this limit for the flow equation is the so-called conformal truncation, or conformally reduced gravity model [45,[61][62][63][64]. Conversely, since any symmetric two-tensor can be split uniquely into its trace and trace-free part:…”

Section: Jhep06(2016)012mentioning

confidence: 99%

“…While this has the same origin as the DeWitt supermetric [60] we find that for both schemes it is actually determined by the other choices we make (and for the Weyl scheme also by the fixed-point ratio s(ω * ) of the couplings). We only touched briefly on the special values j = ∞ and j = −1/D, which correspond to the conformal truncation [45,[61][62][63][64] and unimodular gravity [65][66][67][68] respectively. Since these variants can thus be naturally incorporated, it would be very interesting to develop them further.…”

Section: Jhep06(2016)012mentioning

confidence: 99%

Manifestly diffeomorphism invariant classical Exact Renormalization Group

Morris

Preston

2016

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.