Dimension and dimensional reduction in quantum gravity

Carlip, Steven

doi:10.1088/1361-6382/aa8535

Cited by 124 publications

(155 citation statements)

References 194 publications

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“…However, this theory space exhibits dimensional reduction. Dynamical dimensional reduction at high energies is an intriguing phenomenon in several models of quantum gravity, see, e.g., [125], that are four-dimensional at large scales. In tensor models, dimensional reduction differs in that it appears to be realized at certain classes of fixed points in rank-3 and rank-4 models, such that the continuum limit is not a candidate for three-or four-dimensional quantum gravity.…”

Section: A Dimensional Reduction In Tensor Modelsmentioning

confidence: 99%

Status of Background-Independent Coarse Graining in Tensor Models for Quantum Gravity

2019

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A background-independent route towards a universal continuum limit in discrete models of quantum gravity proceeds through a background-independent form of coarse graining. This review provides a pedagogical introduction to the conceptual ideas underlying the use of the number of degrees of freedom as a scale for a Renormalization Group flow. We focus on tensor models, for which we explain how the tensor size serves as the scale for a background-independent coarse-graining flow. This flow provides a new probe of a universal continuum limit in tensor models. We review the development and setup of this tool and summarize results in the 2-and 3-dimensional case. Moreover, we provide a step-by-step guide to the practical implementation of these ideas and tools by deriving the flow of couplings in a rank-4-tensor model. We discuss the phenomenon of dimensional reduction in these models and find tentative first hints for an interacting fixed point with potential relevance for the continuum limit in four-dimensional quantum gravity.

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Section: A Dimensional Reduction In Tensor Modelsmentioning

confidence: 99%

Status of Background-Independent Coarse Graining in Tensor Models for Quantum Gravity

2019

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“…Moreover, in a gravitational theory, it is rather natural to ask how geometric quantities, like the volume of a submanifold, behave at the quantum level. Indeed, even if such quantities are not true (diffeomorphism invariant) observables, their study may hint at the presence of certain general features of the underlying quantum theory, such as the dynamical dimensional reduction, which has been already observed via different criteria and means in the literature [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Geometric operators in the asymptotic safety scenario for quantum gravity

Becker

Pagani

2019

Phys. Rev. D

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We consider geometric operators, such as the geodesic length and the volume of hypersurfaces, in the context of the Asymptotic Safety scenario for quantum gravity. We discuss the role of these operators from the Asymptotic Safety perspective, and compute their anomalous dimensions within the Einstein-Hilbert truncation. We also discuss certain subtleties arising in the definition of such geometric operators. Our results hint to an effective dimensional reduction of the considered geometric operators.Given the ansatz (2.16), one can show that the scaling operators of the theory have dimension, quantum corrections included, given by the eigenvalues of the matrix [66]Whenever a dot appears, as in J · χ, deWitt summation and integration convention is understood, i.e., J · χ = d d x J a (x) χ a (x).

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“…analyzing spacetimes resulting from different approaches to quantum gravity, see, e.g., [18,19] for a recent compilation. Hereby, different attempts toward quantum gravity typically see a dimensional reduction when going from the infrared to the ultraviolet.…”

Section: Introductionmentioning

confidence: 99%

Spectral dimension as a tool for analyzing nonperturbative propagators

2019

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We derive general properties of the scale-dependent effective spectral dimensions of nonperturbative gauge boson propagators as they appear as solutions from different methods in Yang-Mills theories. In the ultraviolet and for short timescales the anomalous dimensions of the propagators lead to a slight decrease of the spectral dimension as compared to the one of a free propagator. Lowering the momentum scale, the spectral dimension decreases further. The class of propagators which display a maximum at Euclidean momenta, and thus violate positivity, always approaches a spectral dimension of one for large times. We also show that the longest time intervals are not related to the deep infrared but to the momentum scale defined by the position of the maximum.

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Dimension and dimensional reduction in quantum gravity

Cited by 124 publications

References 194 publications

Status of Background-Independent Coarse Graining in Tensor Models for Quantum Gravity

Status of Background-Independent Coarse Graining in Tensor Models for Quantum Gravity

Geometric operators in the asymptotic safety scenario for quantum gravity

Spectral dimension as a tool for analyzing nonperturbative propagators

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