Dimension and Dimensional Reduction in Quantum Gravity

Carlip, Steven

doi:10.3390/universe5030083

Cited by 51 publications

(88 citation statements)

References 277 publications

(326 reference statements)

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“…A wide variety of approaches to quantum gravity have reported a dynamical reduction in the number of spacetime dimensions in the high energy limit (see Refs. [62,63] for a review). Remarkably, these independent approaches almost universally find the same ultraviolet dimensionality of two.…”

Section: Dimensional Reductionmentioning

confidence: 99%

Asymptotically Weyl-invariant gravity

Coumbe¹

2019

Int. J. Mod. Phys. A

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We propose a novel theory of gravity that by construction is renormalizable, evades Ostragadsky's no-go theorem, is locally scale-invariant in the high-energy limit, and equivalent to general relativity in the low-energy limit. The theory is defined by a pure f (R) = R n action in the Palatini formalism, where the dimensionless exponent n runs from a value of two in the high-energy limit to one in the low-energy limit. We show that the proposed model contains no obvious cosmological curvature singularities. The viability of the proposed model is qualitatively assessed using several key criteria. PACS numbers: 04.60.-m, 04.60.Bc IntroductionGeneral relativity is theoretically beautiful, experimentally successful, and defines our best current description of gravity. Its key equations follow almost inevitably from a single symmetry principle and yield predictions that agree with experiment over a vast range of distance scales [1].Yet, general relativity is almost certainly incomplete. One major problem is that it appears to be incompatible with quantum field theory at high energies. Although general relativity has been successfully formulated as an effective quantum field theory at low energies, new divergences appear at each order in the perturbative expansion, leading to a complete loss of predictivity at high energies. Gravity is said to be perturbatively non-renormalizable, a fact demonstrated by explicit calculation at the one-loop level including matter content [2], and at the two-loop level without matter [3]. This behaviour stems from the fact that the gravitational coupling introduces a length scale into the theory so that higher-order corrections in a perturbative expansion come with ever-increasing powers of the cut-off scale.Higher-order actions have been explored as a possible solution to this problem [4]. Explicit calculations show that Lagrangians quadratic in the curvature tensor are renormalizable [5]. However, quadratic theories of gravity are not hailed as the theory of quantum gravity because they are not typically unitary, often containing unphysical ghost modes [5]. Higher-order theories are also generally unstable, violating a powerful no-go theorem first proposed by Ostragadsky [6]. Ostrogradsky's theorem proves that there is a fatal linear instability in any Hamiltonian associated with Lagrangians which depend on two or more time derivatives. This result helps explain the otherwise mysterious fact that the fundamental laws of physics seem to include at most two time derivatives [7]. The only higher-order theories that are both stable and unitary are f (R) theories, in which the Lagrangian is a general function f of the Ricci scalar R [8].Since f (R) gravity is not a single theory but a potentially infinite set of theories, one for each particular function f (R), we must identify a principle capable of selecting a specific function f (R). We contend that this principle should be local scale invariance. One reason for this is that scale-invariant theories of gravity are gauge theories [9,10]. ...

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Section: Dimensional Reductionmentioning

confidence: 99%

Asymptotically Weyl-invariant gravity

Coumbe¹

2019

Int. J. Mod. Phys. A

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“…In this study I focused on constructing and making practical use of an axiomatic basis for MHA from biological considerations alone. Nonetheless, it will be interesting to study whether there are applicable theoretical treatments of low-dimensional topological objects, such as from mathematical knot theory [e.g., Blair and Tomova (2013)] or from models of quantum gravity in physics [e.g., Carlip (2017)]. If so there may exist additional mathematical tools that can be adapted for the alignment of two dimensional biological sequence homology.…”

Section: Mha Widths Are Not Additivementioning

confidence: 99%

Maximal homology alignment: A new method based on two-dimensional homology

Erives

2019

Preprint

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Maximal homology alignment is a new biologically-relevant approach to DNA sequence alignment that embraces microparalogy. It departs from the current method of gapped alignment, which uses a simple, binary state model of nucleotide position. In gapped alignment nucleotide positions have either no relationship (1-to-None) or else orthological relationship (1-to-1) with nucleotides in other sequences. Maximal homology alignment, however, allows additional states such as 1-to-Many and Many-to-Many, thus modeling both orthological and paralogical relationships, which together comprise the main homology types. Maximal homology alignment collects dispersed microparalogy into the same alignment columns on multiple rows, and thereby generates a two-dimensional representation of a single sequence. Sequence alignment then proceeds as the alignment of two-dimensional topological objects. The operations of producing and aligning two dimensional auto-alignments motivate a need for tests of two dimensional homological integrity that are both necessary and sufficient. Here, I work out and implement basic principles for computationally handling the two dimensions of positional homology, which are inherent to biological sequences due to replication slippage and related errors. I then show that maximal homology alignment is more suited and more informative than gapped alignment for modeling the evolution of genetic sequences, which harbor large numbers of small insertions and deletions originating as local microparalogy. These results show that both conserved and non-conserved genomic sequences are imbued with a signature of replication slippage that is absent from their random permutations. KEYWORDS dimensionality; DNA microfoam; Drosophila; enhancer DNAs; gapped alignment (GA); maximal homology alignment (MHA); positional homology; replication slippage; tandem repeats S equences of covalently-linked nucleotides and their evolutionary relationships are the basis of gene homology. The smallest possible scale to ascribe such homology is that of individual nucleotide positions ("site positional homology"). Of course this is possible only in the context of homological inference based on multiple nucleotide positions in a sequence.By studying the function and evolution of regulatory DNA sequences (transcriptional enhancers in Ciona and Drosophila), which are not constrained by rigid, protein-coding, triplet reading frames (Erives et al. Brittain et al. 2014;Stroebele and Erives 2016), I conclude that site positional homology is incorrectly handled by gapped alignment (GA). GA was originally adopted by necessity in order to compare protein sequences of divergent lengths (Braunitzer's gappy comparisons of α-and β-hemoglobin

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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%

“…(19) applies for arbitrary complex p 2 . In general, Eq (19). holds (in the absence of complex poles), but a necessary condition for a physical particle is that ρ(s) is not negative for any s. Thus, if one can show what ρ(s) is negative somewhere, the particle is removed from the physical state space.…”

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confidence: 99%

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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 51 publications

References 277 publications

Asymptotically Weyl-invariant gravity

Asymptotically Weyl-invariant gravity

Maximal homology alignment: A new method based on two-dimensional homology

Spectral dimension as a tool for analyzing nonperturbative propagators

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