Spontaneous dimensional reduction?

Carlip, Steven

doi:10.1063/1.4756963

Cited by 18 publications

(27 citation statements)

References 55 publications

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“…In other words, vacuum fluctuations seem to be fundamental to balance the fragmentation of spacetime in the ultraviolet [37]. An UV completion of the spectral action could be achieved through the Asymptotic Safety mechanism [47,59], which seems a natural choice given the field content and symmetries of the model, may lead to D S (T ) interpolating from four to two, while still keeping the non-polynomial momentum dependence in the propagators.…”

Section: Discussionmentioning

confidence: 99%

“…By now, this "observable" has been computed in many approaches to quantum gravity and a number of quantum gravity inspired models. A common feature shared by many of these studies is a "dynamical dimensional reduction" from a classical spacetime with D S (T ) = 4 at macroscopic scales to D S (T ) = 2 [36,37]. The widespread use of D S (T ) throughout the quantum gravity community then calls for a detailed understanding which (quantum) features of a model are actually encoded in D S (T ).…”

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: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Spectral dimensions from the spectral action

2015

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“…In addition, it has recently been found that Causal Dynamical Triangulations [2], Asymptotic Safety [3], Loop Quantum Gravity [4], Hořava-Lifshitz Theory [5] and also Liouville Quantum Gravity [6] predict the same spectral dimension of 2 [7]. It has been suggested that such an agreement must contain some hints of a full theory of quantum gravity [8]. One exceptional theory is Non-commutative Geometry [9] which predicts spectral dimension of 3 in the ultraviolet regime.…”

Section: Introductionmentioning

confidence: 99%

Spectral dimension of bosonic string theory

Moore

Satheeshkumar

2014

Phys. Rev. D

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Given that the scale of quantum gravity is not experimentally accessible, one naturally resorts to mathematical consistency as a measure for a good candidate theory to replace General Relativity at high energies. Reproducing the semi-classical results of black hole entropy has become a standard test for any prospective theory of quantum gravity. It is often argued that another such commonality, albeit less known, is the similar fractal behaviour. It is shown that many, if not all, approaches to quantum gravity predict a spectral dimension of 2 in ultraviolet regime. In this paper, by computing the heat kernel, we show that the spectral dimension of closed bosonic string theory is 26. We discuss the implications of this disparity.

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“…Dimensional flows are a feature commonly encountered in virtually all approaches to quantum gravity and quantum gravity inspired models [1,2]. The most prominent example of a dimensional flow occurs in Kaluza-Klein theories where the dimensionality of spacetime increases below the compactification scale.…”

Section: Introductionmentioning

confidence: 99%

“…2 We will show that different types of dimensional flows leave distinct signatures in the detector rates. In particular, in the case of dimensional reduction at high energies, one finds a suppression of the rates, whereas for a dimensional enhancement at high energies, as in Kaluza-Klein models, the rate increases.…”

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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Spontaneous dimensional reduction?

Cited by 18 publications

References 55 publications

Spectral dimensions from the spectral action

Spectral dimensions from the spectral action

Spectral dimension of bosonic string theory

Quantum gravity signatures in the Unruh effect

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