Anomalous dimension in three-dimensional semiclassical gravity

Alesci, Emanuele; Arzano, Michele

doi:10.1016/j.physletb.2011.12.026

Cited by 43 publications

(63 citation statements)

References 55 publications

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“…The vanishing of the spectral dimension, D S (T ) = 0, is in agreement with the previous computations obtained for other non-commutative spacetimes [58]. This is a welcome and surprising result, since the non-commutative nature of our spectral triple construction differs substantially from that of [58].…”

Section: Discussionsupporting

confidence: 90%

“…This is a welcome and surprising result, since the non-commutative nature of our spectral triple construction differs substantially from that of [58]. Aside for the limiting case of vanishing spectral dimension, both results display the same qualitative features: The spectral dimension interpolates between the topological dimension and zero, and has a local maximum situated close to a transition scale.…”

Section: Discussionmentioning

confidence: 54%

“…Finally, D S (T ) may be modified through non-trivial quantum fluctuations of spacetime predicted by a fundamental theory of gravity. This set includes the multifractal spacetimes occurring in the gravitational Asymptotic Safety program [33,[45][46][47][48], the microscopic structure of spacetime within Loop Quantum Gravity [49][50][51][52][53][54], Causal Set Theory [55] or the propagation of particles on κ-Minkowski [56,57] and other non-commutative spaces [58].…”

Section: Introductionmentioning

confidence: 99%

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Spectral dimensions from the spectral action

2015

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The generalised spectral dimension DS(T ) provides a powerful tool for comparing different approaches to quantum gravity. In this work, we apply this formalism to the classical spectral actions obtained within the framework of almost-commutative geometry. Analysing the propagation of spin-0, spin-1 and spin-2 fields, we show that a non-trivial spectral dimension arises already at the classical level. The effective field theory interpretation of the spectral action yields plateaustructures interpolating between a fixed spin-independent DS(T ) = dS for short and DS(T ) = 4 for long diffusion times T . Going beyond effective field theory the spectral dimension is completely dominated by the high-momentum properties of the spectral action, yielding DS(T ) = 0 for all spins. Our results support earlier claims that high-energy bosons do not propagate.

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Section: Discussionsupporting

confidence: 90%

Section: Discussionmentioning

confidence: 54%

Section: Introductionmentioning

confidence: 99%

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Spectral dimensions from the spectral action

2015

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“…The transition between the two regimes varies depending on the model but it is continuous in general. Examples include causal dynamical triangulations [5][6][7], asymptotically safe quantum gravity [8,9], loop quantum gravity and spin foams [10][11][12], Hořava-Lifshitz gravity [7,9,13], noncommutative geometry [14][15][16] and κ-Minkowski spacetime [17,18], nonlocal quantum gravity [19], Stelle's gravity [20], spacetimes with black holes [21][22][23], fuzzy spacetimes [24], random combs [25,26], random multigraphs [27,28], and causal sets [29].…”

Section: A Dimensional Flow and Multiscale Theoriesmentioning

confidence: 99%

Standard Model in multiscale theories and observational constraints

2016

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We construct and analyze the Standard Model of electroweak and strong interactions in multiscale spacetimes with (i) weighted derivatives and (ii) q-derivatives. Both theories can be formulated in two different frames, called fractional and integer picture. By definition, the fractional picture is where physical predictions should be made. (i) In the theory with weighted derivatives, it is shown that gauge invariance and the requirement of having constant masses in all reference frames make the Standard Model in the integer picture indistinguishable from the ordinary one. Experiments involving only weak and strong forces are insensitive to a change of spacetime dimensionality also in the fractional picture, and only the electromagnetic and gravitational sectors can break the degeneracy. For the simplest multiscale measures with only one characteristic time, length and energy scale t Ã , l Ã and E Ã , we compute the Lamb shift in the hydrogen atom and constrain the multiscale correction to the ordinary result, getting the absolute upper bound t Ã < 10 −23 s. For the natural choice α 0 ¼ 1=2 of the fractional exponent in the measure, this bound is strengthened to t Ã < 10 −29 s, corresponding to l Ã < 10 −20 m and E Ã > 28 TeV. Stronger bounds are obtained from the measurement of the fine-structure constant.(ii) In the theory with q-derivatives, considering the muon decay rate and the Lamb shift in light atoms, we obtain the independent absolute upper bounds t Ã < 10 −13 s and E Ã > 35 MeV. For α 0 ¼ 1=2, the Lamb shift alone yields t Ã < 10

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“…Profiles of d S overshooting the Hausdorff and topological dimensions of space appear also in lattice-based [15] and noncommutative geometries [22]. Due to the presence of a characteristic scale (the noncommutative fundamental scale [22], or the lattice cell size 11 [15], or the label-dependent length of the edges of a labeled graph [15]), the geometric information in the diffusion equation determines a nontrivial spatial generator. On the other hand, the diffusion operator is assumed to be the integer one ∂ σ , so these models roughly mimic certain properties of Lévy processes.…”

Section: A Multiscale Lévy Processmentioning

confidence: 99%

Diffusion in multiscale spacetimes

Calcagni

2013

Phys. Rev. E

140

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We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are partly based on the literature in probability and percolation theory but their physical interpretation here is different since they apply to quantum spacetime itself. The case of multiscale (in particular, multifractal) spacetimes is then considered through a number of examples, and the most general spectral-dimension profile of multifractional spaces is constructed.

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Anomalous dimension in three-dimensional semiclassical gravity

Cited by 43 publications

References 55 publications

Spectral dimensions from the spectral action

Spectral dimensions from the spectral action

Standard Model in multiscale theories and observational constraints

Diffusion in multiscale spacetimes

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