A functional RG equation for the c-function

Codello, Alessandro; D'Odorico, Giulio; Pagani, Carlo

doi:10.1007/jhep07(2014)040

Cited by 28 publications

(76 citation statements)

References 39 publications

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“…This bimetric structure has first been studied in [46][47][48]. Here, we extend the recent analysis in [32] to include matter fields. At the level of the Einstein-Hilbert truncation, we need to introduce the graviton and matter anomalous dimensions, in order to provide a consistent closure of the flow equation from which we will extract the β functions of the background field G and Λ.…”

Section: B Background Field and Fluctuation Fieldmentioning

confidence: 60%

“…We adopt the traditional perturbative convention of rescaling the metric fluctuation field to make it canonically normalized (this convention was also used in a functional RG context in [32]). This split allows to gaugefix with respect to the background field, and demanding background-field gauge invariance ensures gauge invariance of the full effective action Γ.…”

Section: B Background Field and Fluctuation Fieldmentioning

confidence: 99%

“…The first contribution is evaluated using the diagrams listed in [32]. We project the resulting tensorial structure along the tensor K which is the structure of the graviton propagator in the gauge α = 1 that we are using here.…”

Section: B Background Field and Fluctuation Fieldmentioning

confidence: 99%

“…The main novel computational result of this paper are the formulas for the anomalous dimensions η h , η S , η D and η V . Following [32], the gravitational contribution to the graviton anomalous dimension can be written in the form…”

Section: Beta Functionsmentioning

confidence: 99%

“…Evidence for the existence of a gravitational fixed point with a finite number of relevant directions has been collected with a variety of tools, but in recent years most progress has come from functional Renormalization Group methods, whose application to gravity has been pioneered in [18]. Various nonperturbative truncations of the RG flow indicate the existence of an interacting fixed point [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. Recent results also suggest the existence of an infrared fixed point [35][36][37].…”

Section: Introductionmentioning

confidence: 99%

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Matter matters in asymptotically safe quantum gravity

2014

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We investigate the compatibility of minimally coupled scalar, fermion and gauge fields with asymptotically safe quantum gravity, using nonperturbative functional Renormalization Group methods. We study d = 4, 5 and 6 dimensions and within certain approximations find that for a given number of gauge fields there is a maximal number of scalar and fermion degrees of freedom compatible with an interacting fixed point at positive Newton coupling. The bounds impose severe constraints on grand unification with fundamental Higgs scalars. Supersymmetry and universal extra dimensions are also generally disfavored. The standard model and its extensions accommodating right-handed neutrinos, the axion and dark-matter models with a single scalar are compatible with a fixed point.

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Section: B Background Field and Fluctuation Fieldmentioning

confidence: 60%

Section: B Background Field and Fluctuation Fieldmentioning

confidence: 99%

Section: B Background Field and Fluctuation Fieldmentioning

confidence: 99%

Section: Beta Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Matter matters in asymptotically safe quantum gravity

2014

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Asymptotic safety and the cosmological constant

Falls

2016

J. High Energ. Phys.

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Abstract:We study the non-perturbative renormalisation of quantum gravity in four dimensions. Taking care to disentangle physical degrees of freedom, we observe the topological nature of conformal fluctuations arising from the functional measure. The resulting beta functions possess an asymptotically safe fixed point with a global phase structure leading to classical general relativity for positive, negative or vanishing cosmological constant. If only the conformal fluctuations are quantised we find an asymptotically safe fixed point predicting a vanishing cosmological constant on all scales. At this fixed point we reproduce the critical exponent, ν = 1/3, found in numerical lattice studies by Hamber. Returning to the full theory we find that by setting the cosmological constant to zero the critical exponent agrees with the conformally reduced theory. This suggests the fixed point may be physical while hinting at solution to the cosmological constant problem.

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The unitary conformal field theory behind 2D Asymptotic Safety

Nink

Reuter

2016

J. High Energ. Phys.

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Being interested in the compatibility of Asymptotic Safety with Hilbert space positivity (unitarity), we consider a local truncation of the functional RG flow which describes quantum gravity in d > 2 dimensions and construct its limit of exactly two dimensions. We find that in this limit the flow displays a nontrivial fixed point whose effective average action is a non-local functional of the metric. Its pure gravity sector is shown to correspond to a unitary conformal field theory with positive central charge c = 25. Representing the fixed point CFT by a Liouville theory in the conformal gauge, we investigate its general properties and their implications for the Asymptotic Safety program. In particular, we discuss its field parametrization dependence and argue that there might exist more than one universality class of metric gravity theories in two dimensions. Furthermore, studying the gravitational dressing in 2D asymptotically safe gravity coupled to conformal matter we uncover a mechanism which leads to a complete quenching of the a priori expected Knizhnik-Polyakov-Zamolodchikov (KPZ) scaling. A possible connection of this prediction to Monte Carlo results obtained in the discrete approach to 2D quantum gravity based upon causal dynamical triangulations is mentioned. Similarities of the fixed point theory to, and differences from, non-critical string theory are also described. On the technical side, we provide a detailed analysis of an intriguing connection between the Einstein-Hilbert action in d > 2 dimensions and Polyakov's induced gravity action in two dimensions.

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A functional RG equation for the c-function

Cited by 28 publications

References 39 publications

Matter matters in asymptotically safe quantum gravity

Matter matters in asymptotically safe quantum gravity

Asymptotic safety and the cosmological constant

The unitary conformal field theory behind 2D Asymptotic Safety

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