Asymptotic Freedom in Hořava-Lifshitz Gravity

D'Odorico, Giulio; Saueressig, Frank; Schutten, Marrit

doi:10.1103/physrevlett.113.171101

Cited by 57 publications

(55 citation statements)

References 37 publications

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“…Asymptotic Safety has also been showed to play a significant role in understanding of the phase diagram of the anisotropic theories of gravity, dubbed Hořava-Lifshitz gravity [53]. Hořava-Lifshitz gravity is conjectured to be perturbatively renormalizable and the fixed point structure underlying this conjecture as well as its relation to the Asymptotic Safety proposal has recently been clarified [54].…”

Section: Asymptotic Safety: a Primermentioning

confidence: 98%

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RG flows of Quantum Einstein Gravity in the linear-geometric approximation

2015

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a b s t r a c tWe construct a novel Wetterich-type functional renormalization group equation for gravity which encodes the gravitational degrees of freedom in terms of gauge-invariant fluctuation fields. Applying a linear-geometric approximation the structure of the new flow equation is considerably simpler than the standard Quantum Einstein Gravity construction since only transverse-traceless and trace part of the metric fluctuations propagate in loops. The geometric flow reproduces the phase-diagram of the Einstein-Hilbert truncation including the non-Gaussian fixed point essential for Asymptotic Safety. Extending the analysis to the polynomial f (R)-approximation establishes that this fixed point comes with similar properties as the one found in metric Quantum Einstein Gravity; in particular it possesses three UV-relevant directions and is stable with respect to deformations of the regulator functions by endomorphisms.

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Section: Asymptotic Safety: a Primermentioning

confidence: 98%

“…The beta functions (53) together with the expression for the anomalous dimension of Newton's constant (54) constitute the main result of this section. For the remainder of this section we then study the properties of the flow implied by (52).…”

Section: The Einstein-hilbert Truncationmentioning

confidence: 99%

RG flows of Quantum Einstein Gravity in the linear-geometric approximation

2015

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“…Yet, the projectable version propagates an additional scalar that becomes nonperturbative in the IR. As the non-projectable version features a larger number of couplings, asymptotic freedom has only been established in 2 + 1 [146] dimensions and not 3 + 1, as well as in the large N limit for N scalars coupled to Horava gravity [147]. Constraints from pulsars [148] and gravitational waves from a neutron-star merger [149] constrain these models.…”

Section: Asymptotically Safe Quantum Gravity 41 Status Of Asymptoticmentioning

confidence: 99%

An Asymptotically Safe Guide to Quantum Gravity and Matter

Eichhorn

2019

Front. Astron. Space Sci.

237

240

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Asymptotic safety generalizes asymptotic freedom and could contribute to understanding physics beyond the Standard Model. It is a candidate scenario to provide an ultraviolet extension for the effective quantum field theory of gravity through an interacting fixed point of the Renormalization Group. Recently, asymptotic safety has been established in specific gauge-Yukawa models in four dimensions in perturbation theory, providing a starting point for asymptotically safe model building. Moreover, an asymptotically safe fixed point might even be induced in the Standard Model under the impact of quantum fluctuations of gravity in the vicinity of the Planck scale. This review contains an overview of the key concepts of asymptotic safety, its application to matter and gravity models, exploring potential phenomenological implications and highlighting open questions. Invitation to asymptotic safetyAsymptotic safety [1] is a quantum-field theoretic paradigm providing an ultraviolet (UV) extension or completion for effective field theories. The high-momentum regime of an asymptotically safe theory is scale invariant, cf. Fig. 1. It is governed by a fixed point of the Renormalization Group (RG) flow of couplings. As such, asymptotic safety is an example of a fruitful transfer of ideas from statistical physics to highenergy physics: In the former, interacting RG fixed points provide universality classes for continuous phase transitions [2,3], in the latter these generalize asymptotic freedom to a scale-invariant UV completion with residual interactions. This paradigm is being explored for physics beyond the Standard Model in several promising ways. Following the discovery of perturbative asymptotic safety in weakly-coupled gauge-Yukawa models in four dimensions [4], the search for asymptotically safe extensions of the Standard Model with new degrees of freedom close to the electroweak scale is ongoing. Mechanisms for asymptotic safety also exist in nonrenormalizable settings, making it a candidate paradigm for quantum gravity [1,5]. After the discovery of the Higgs boson [6,7], we know that the Standard Model can consistently be extended up to the Planck scale [8,9,10]. Hence, the interplay of the Standard Model with quantum fluctuations of gravity within a quantum field theoretic setting is under active exploration.This review aims at providing an introduction to asymptotic safety for non-experts, highlighting mechanisms that generate asymptotically safe physics, explaining how these could play a role in settings relevant for high-energy physics and discussing open questions of (potentially) asymptotically safe models. An extensive bibliography is intended to serve as a guide to further reading, providing more comprehensive and in-depth answers to many points only touched upon briefly here. * a.eichhorn@thphys.uni-heidelberg.de arXiv:1810.07615v2 [hep-th]

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“…Indeed, at the moment there is no definite evidence that the theory is fully quantum renormalizable (even if some evidence in this direction has been recently revealed in Ref. [8]), and the renormalizability is only supported by power-counting arguments.…”

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confidence: 99%

“…However, taking into account the extra terms in W extra , it is straightforward to see that power-counting renormalizability is generically preserved in the tensor sector. In fact, considering tensor perturbations we find that the operators R ij ∇ 2 R ij in V (6) and ∇ 2 R kl ∇ 2 R kl in V (8) generically yield non-trivial contributions, respectively, at sixth-and eighth-order, to the dispersion relation of the spin-2 graviton:…”

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On power-counting renormalizability of Hořava gravity with detailed balance

Vernieri

2015

Phys. Rev. D

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We consider the version of Hořava gravity where "detailed balance" is consistently implemented, so as to limit the huge proliferation of couplings in the full theory and obtain healthy dynamics at low energy. Since a superpotential which is third-order in spatial derivatives is not sufficient to guarantee the power-counting renormalizability of the spin-0 graviton, one needs to go an order beyond in derivatives, building a superpotential up to fourth-order spatial derivatives. Here we perturb the action to quadratic order around flat space and show that the power-counting renormalizability of the spin-0 graviton is achieved only by setting to zero a specific coupling of the theory, while the spin-2 graviton is always power-counting renormalizable for any choice of the couplings. This result raises serious doubts about the use of detailed balance.PACS numbers: 04.60.-m, 04.50. Kd, 11.30.Cp Hořava gravity [1,2] has attracted a lot of attention since it was first proposed, as it encodes all the necessary ingredients to be both a renormalizable theory of gravity and a phenomenologically viable one (see Refs. [3][4][5] for some reviews).The fundamental aim of the theory is to be an ultraviolet (UV) completion of general relativity, pursued by abandoning the local Lorentz invariance. It is based on the idea of modifying the graviton propagator by adding to the gravitational action higher-order spatial derivatives without adding higher-order time derivatives. In this way one can obtain a power-counting renormalizable theory [6,7]. Indeed, at the moment there is no definite evidence that the theory is fully quantum renormalizable (even if some evidence in this direction has been recently revealed in Ref.[8]), and the renormalizability is only supported by power-counting arguments.Since the theory treats space and time on different footing, it is naturally constructed in terms of a preferred foliation of spacetime, leading to violations of Lorentz symmetry at all scales. The theory is built using an ADM decomposition of spacetime,where N is the lapse function, N i the shift vector, and g ij the induced three-dimensional metric on the spacelike hypersurfaces.The most general action of Hořava gravity can be written as follows:whereis the kinetic term, which is quadratic in the time derivatives, k is a coupling of suitable dimensions, K ij is the extrinsic curvature of the spacelike hypersurfaces,K = g ij K ij is its trace, ∇ i is the covariant derivative associated with g ij , λ is a dimensionless coupling, and G ijkl is the generalized DeWitt "metric on the space of metrics", which is written in terms of the induced metric g ij asThe potential term isand it includes all the operators built with the metric and the lapse compatibly with the invariance of the theory under foliation-preserving diffeomorphisms, i.e., t →t(t), x i →x i (t, x i ). The most general action includes a very large number of operators ∼ O(10 2 ) that are allowed by the symmetry. This makes the theory intractable and compromises predictability in th...

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Asymptotic Freedom in Hořava-Lifshitz Gravity

Cited by 57 publications

References 37 publications

RG flows of Quantum Einstein Gravity in the linear-geometric approximation

RG flows of Quantum Einstein Gravity in the linear-geometric approximation

An Asymptotically Safe Guide to Quantum Gravity and Matter

On power-counting renormalizability of Hořava gravity with detailed balance

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