Scaling exponents in quantum gravity near two dimensions

Kawai, Hiroyuki; Kitazawa, Yoshihisa; Ninomiya, M.

doi:10.1016/0550-3213(93)90246-l

Cited by 133 publications

(162 citation statements)

References 10 publications

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“…A subclass of these geometries is the piecewise linear geometries and a further subclass is the piecewise linear geometries defined by triangulations obtained by gluing together equilateral D-simplices such that they 1 The idea of a time foliation and the fact that there exists a related unitary time evolution are features which CDT shares with Hořava-Lifshitz gravity [6][7][8][9]. However, no spatial higher derivative terms are explicitly added to the action, like in Hořava-Lifshitz gravity, and it is possible that fixed points of the lattice theory can be identified with the non-trivial UV fixed points conjectured in the asymptotic safety scenario suggested by Weinberg [10] and investigated in [11][12][13][14][15][16][17][18][19][20][21][22].…”

Section: Cdt and The Cdt Transfer Matrixmentioning

confidence: 99%

The transfer matrix in four-dimensional CDT

Ambjørn¹,

Gizbert-Studnicki

Görlich

et al. 2012

J. High Energ. Phys.

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Abstract:The Causal Dynamical Triangulation model of quantum gravity (CDT) has a transfer matrix, relating spatial geometries at adjacent (discrete lattice) times. The transfer matrix uniquely determines the theory. We show that the measurements of the scale factor of the (CDT) universe are well described by an effective transfer matrix where the matrix elements are labeled only by the scale factor. Using computer simulations we determine the effective transfer matrix elements and show how they relate to an effective minisuperspace action at all scales.

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Section: Cdt and The Cdt Transfer Matrixmentioning

confidence: 99%

The transfer matrix in four-dimensional CDT

Ambjørn¹,

Gizbert-Studnicki

Görlich

et al. 2012

J. High Energ. Phys.

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“…It depends, however, on the parametrization of the metric. In the linear parametrization, g µν =ḡ µν + h µν , it is given by [1, 8, 22, 24-26, 44, 45, 48, 49] 34) while the exponential parametrization [59], g µν =ḡ µρ (e h ) ρ ν , leads to [22,26,[50][51][52][53][54][55][56][57][58] …”

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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“…If so, the high energy behaviour of gravity is governed by near-conformal scaling in the vicinity of the fixed point in a way which circumnavigates the virulent ultraviolet (UV) divergences encountered within standard perturbation theory. Indications in favour of an ultraviolet fixed point are based on renormalisation group studies in four and higher dimensions [6,7,8,9,10,11,12,13,14,15,16,17,18], dimensional reduction techniques [19,20], renormalisation group studies in lower dimensions [1,21,22,23,24], four-dimensional perturbation theory in higher derivative gravity [25], large-N expansions in the matter fields [26], and lattice simulations [27,28,29].…”

Section: Introductionmentioning

confidence: 99%

On fixed points of quantum gravity

Litim

2006

AIP Conference Proceedings

111

182

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We review the asymptotic safety scenario for quantum gravity and the role and implications of an underlying ultraviolet fixed point. We discuss renormalisation group techniques employed in the fixed point search, analyse the main picture at the example of the Einstein-Hilbert theory, and provide an overview of the key results in four and higher dimensions. We also compare findings with recent lattice simulations and evaluate phenomenological implications for collider experiments. From Quantum to Emergent Gravity: Theory and Phenomenology

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Scaling exponents in quantum gravity near two dimensions

Cited by 133 publications

References 10 publications

The transfer matrix in four-dimensional CDT

The transfer matrix in four-dimensional CDT

The unitary conformal field theory behind 2D Asymptotic Safety

On fixed points of quantum gravity

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