Quantum Einstein gravity

Reuter, Martin; Saueressig, Frank

doi:10.1088/1367-2630/14/5/055022

Cited by 355 publications

(482 citation statements)

References 156 publications

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“…By now a large variety of truncations have been studied to support the existence of a NGFP of metric gravity, including for instance terms of higher orders in the curvature or actions that couple gravity to matter [18][19][20][21]. (2).…”

Section: Jhep02(2016)167mentioning

confidence: 99%

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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Section: Jhep02(2016)167mentioning

confidence: 99%

The unitary conformal field theory behind 2D Asymptotic Safety

Nink

Reuter

2016

J. High Energ. Phys.

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“…2 First results on the RG flow on T pHL including Diff(M)-breaking interactions will be reported elsewhere [36].…”

Section: Introductionmentioning

confidence: 99%

“…Within the realm of quantum field theory there are currently two proposals that receive a lot of attention. Quantum Einstein Gravity (QEG) [1,2,3,4] is based on Weinberg's Asymptotic Safety scenario [5,6] and suggests that gravity could be a non-perturbatively renormalizable quantum field theory. In this case the UVcompletion of the theory is provided by a non-Gaussian fixed point (NGFP) of the renormalization group (RG) flow.…”

Section: Introductionmentioning

confidence: 99%

“…Here, Γ (2) k denotes the second functional derivative of the effective average action with respect to the fluctuation fields φ at fixed backgroundφ and Tr contains a sum over all fields of the theory and an integration over loop-momenta. Furthermore, R k is a matrix-valued IR cutoff, which provides a k-dependent mass term for fluctuations with momenta p 2 < k 2 .…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, R k is a matrix-valued IR cutoff, which provides a k-dependent mass term for fluctuations with momenta p 2 < k 2 . The interplay between the full regularized propagator Γ (2) k + R k −1 and k∂ k R k ensures that the Tr receives contributions from a small p 2 -interval around k 2 ≈ p 2 only, rendering the trace contribution finite.…”

Section: Introductionmentioning

confidence: 99%

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A functional renormalization group equation for foliated spacetimes

Rechenberger

Saueressig

2013

J. High Energ. Phys.

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We derive an exact functional renormalization group equation for the projectable version of Hořava-Lifshitz gravity. The flow equation encodes the gravitational degrees of freedom in terms of the lapse function, shift vector and spatial metric and is manifestly invariant under background foliation-preserving diffeomorphisms. Its relation to similar flow equations for gravity in the metric formalism is discussed in detail, and we argue that the space of action functionals, invariant under the full diffeomorphism group, forms a subspace of the latter invariant under renormalization group transformations. As a first application we study the RG flow of the Newton constant and the cosmological constant in the ADM formalism. In particular we show that the non-Gaussian fixed point found in the metric formulation is qualitatively unaffected by the change of variables and persists also for Lorentzian signature metrics.

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From general relativity to quantum gravity

Ashtekar¹,

Reuter

Rovelli

Mathematical Problems in Theoretical Physics

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In general relativity (GR), spacetime geometry is no longer just a background arena but a physical and dynamical entity with its own degrees of freedom. We present an overview of approaches to quantum gravity in which this central feature of GR is at the forefront. However, the short distance dynamics in the quantum theory are quite different from those of GR and classical spacetimes and gravitons emerge only in a suitable limit. Our emphasis is on communicating the key strategies, the main results and open issues. In the spirit of this volume, we focus on a few avenues that have led to the most significant advances over the past 2-3 decades. 1

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Quantum Einstein gravity

Cited by 355 publications

References 156 publications

The unitary conformal field theory behind 2D Asymptotic Safety

The unitary conformal field theory behind 2D Asymptotic Safety

A functional renormalization group equation for foliated spacetimes

From general relativity to quantum gravity

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