Abstract
The renormalization group flow of unimodular quantum gravity is computed by taking into account the graviton and Faddeev-Popov ghosts anomalous dimensions. In this setting, a ultraviolet attractive fixed point is found. Symmetry-breaking terms induced by the coarse-graining procedure are introduced and their impact on the flow is analyzed. A discussion on the equivalence of unimodular quantum gravity and standard full diffeomorphism invariant theories is provided beyond perturbation theory.
Highlights
Priori riddle between the quantum-field theoretic toolbox and GR
We focus on unimodular gravity and, in the following, we highlight some peculiarities of such a theory and how the functional renormalization group (FRG) should be adapted in this case
Unimodular gravity is an equivalent description of the gravitional field at the classical level with respect to general relativity
Summary
The flow of the 2-point function Γ(k2) can be obtained by acting with two functional derivatives w.r.t. φ on the FRG equation. The r.h.s. of the flow equation for δ2Γk/δb involves 3- and 4-point vertices containing at least one functional derivative w.r.t. the Lautrup-Nakanishi field Vertices with these features are not present in the truncation we are considering. With inclusion of the masses m2k,TT and m2k,σ, we investigate the viability of a UV completion within the extended truncation which includes symmetry-breaking terms This means that we look for fixed point solutions of the partial system of RG equations. The semi-perturbative regime is defined by setting the anomalous dimensions to zero in the functions fTT and fσ, but using the semi-perturbative expressions for ηTT and ησ in the first term on the r.h.s. of eqs.
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