Dimensional reduction in causal set gravity

Carlip, Steven

doi:10.1088/0264-9381/32/23/232001

Cited by 47 publications

(62 citation statements)

References 48 publications

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“…Moreover, dimensional reduction appears as a potentially universal result from different quantum-gravity approaches [80][81][82][83][84][85][86]. Here, we find hints of a different form of effective dimensional reduction in asymptotically safe gravity, which is linked to the effective scaling dimension of matter couplings.…”

Section: Jhep01(2018)030mentioning

confidence: 64%

Upper bound on the Abelian gauge coupling from asymptotic safety

Eichhorn

Versteegen

2018

J. High Energ. Phys.

119

167

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Abstract:We explore the impact of asymptotically safe quantum gravity on the Abelian gauge coupling in a model including a charged scalar, confirming indications that asymptotically safe quantum fluctuations of gravity could trigger a power-law running towards a free fixed point for the gauge coupling above the Planck scale. Simultaneously, quantum gravity fluctuations balance against matter fluctuations to generate an interacting fixed point, which acts as a boundary of the basin of attraction of the free fixed point. This enforces an upper bound on the infrared value of the Abelian gauge coupling. In the regime of gravity couplings which in our approximation also allows for a prediction of the top quark and Higgs mass close to the experimental value [1], we obtain an upper bound approximately 35 % above the infrared value of the hypercharge coupling in the Standard Model.

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Section: Jhep01(2018)030mentioning

confidence: 64%

Upper bound on the Abelian gauge coupling from asymptotic safety

Eichhorn

Versteegen

2018

J. High Energ. Phys.

119

167

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“…The same is true for a causal diffusion process that only proceeds along links in a future-directed fashion where the dimension can be extracted from the meeting probability of two diffusion processes [12]. This dimensional increase has been associated with asymptotic silence [23]. As shown in [24], manifoldlike causal sets do indeed exhibit a discrete asymptotic silence regime, but this in turn can be used to define a new dimension estimator, which does show dimensional reduction.…”

Section: Introductionmentioning

confidence: 93%

Spectral dimension on spatial hypersurfaces in causal set quantum gravity

Eichhorn

Surya

Versteegen

2019

Class. Quantum Grav.

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An important probe of quantum geometry is its spectral dimension, defined via a spatial diffusion process. In this work we study the spectral dimension of a "spatial hypersurface" in a manifoldlike causal set using the induced spatial distance function. In previous work, the diffusion was taken on the full causal set, where the nearest neighbours are unbounded in number. The resulting superdiffusion leads to an increase in the spectral dimension at short diffusion times, in contrast to other approaches to quantum gravity. In the current work, by using a temporal localisation in the causal set, the number of nearest spatial neighbours is rendered finite. Using numerical simulations of causal sets obtained from d = 3 Minkowski spacetime, we find that for a flat spatial hypersurface, the spectral dimension agrees with the Hausdorff dimension at intermediate scales, but shows clear indications of dimensional reduction at small scales, i.e., in the ultraviolet. The latter is a direct consequence of "discrete asymptotic silence" at small scales in causal sets. * eichhorn@sdu.dk

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“…A prototypical example is provided by Causal Set Theory. Here G(p 2 ) interpolates between the standard propagator for a massive scalar field for momenta p 2 below the discretization scale and a nonlocal expression without giving rise to additional poles in the complex p 0 -plane [19,20]. In these cases it is still possible to obtain an explicit formula for the profile function F(E) based on the Källen-Lehmann representation of the two-point function.…”

Section: Detector Rates From the Källen-lehmann Representationmentioning

confidence: 99%

“…The prototypical example for this mechanism is provided by Causal Dynamical Triangulations [3] where a random walk sees a two-dimensional spacetime at short distances while long walks exhibit a four-dimensional behavior [4]. Similar features are encountered in Asymptotic Safety [5][6][7][8][9], Loop Quantum Gravity [10][11][12][13][14][15], Hořava-Lifshitz gravity [16,17], Causal Set Theory [18][19][20], κ-Minkowski space [21][22][23], non-commutative geometry [24,25], non-local gravity theories [26,27], minimal length models [28], and based on the Hagedorn temperature seen by a gas of strings [29].…”

Section: Introductionmentioning

confidence: 99%

Quantum gravity signatures in the Unruh effect

et al. 2016

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We study quantum gravity signatures emerging from phenomenologically motivated multiscale models, spectral actions, and Causal Set Theory within the detector approach to the Unruh effect. We show that while the Unruh temperature is unaffected, Lorentz-invariant corrections to the two-point function leave a characteristic fingerprint in the induced emission rate of the accelerated detector. Generically, quantum gravity models exhibiting dynamical dimensional reduction exhibit a suppression of the Unruh rate at high energy while the rate is enhanced in Kaluza-Klein theories with compact extra dimensions. We quantify this behavior by introducing the "Unruh dimension" as the effective spacetime dimension seen by the Unruh effect and show that it is related, though not identical, to the spectral dimension used to characterize spacetime in quantum gravity. We comment on the physical origins of these effects and their relevance for black hole evaporation.

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Dimensional reduction in causal set gravity

Cited by 47 publications

References 48 publications

Upper bound on the Abelian gauge coupling from asymptotic safety

Upper bound on the Abelian gauge coupling from asymptotic safety

Spectral dimension on spatial hypersurfaces in causal set quantum gravity

Quantum gravity signatures in the Unruh effect

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