The DOI matches its Crossref record; 24 of the 24 references it cites were found in a registry or an index.
Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
Open accessAbstract
We extend the definition of "spectral dimension" d_{s} (usually defined for fractal and lattice geometries) to theories in spacetimes with anisotropic scaling. We show that in gravity with dynamical critical exponent z in D+1 dimensions, the spectral dimension of spacetime is d_{s}=1+D/z. In the case of gravity in 3+1 dimensions with z=3 in the UV which flows to z=1 in the IR, the spectral dimension changes from d_{s}=4 at large scales to d_{s}=2 at short distances. Remarkably, this is the behavior found numerically by Ambjørn et al. in their causal dynamical triangulations approach to quantum gravity.
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Cites
Large Mass Hierarchy from a Small Extra Dimension
Randall, L., & Sundrum, R. (1999) · Physical Review Letters · doi:10.1103/physrevlett.83.3370 · Cited by 9,227
An Alternative to Compactification
Randall, L., & Sundrum, R. (1999) · Physical Review Letters · doi:10.1103/physrevlett.83.4690 · Cited by 7,217
Sachdev, S. (2000) · Cambridge University Press eBooks · doi:10.1017/cbo9780511622540 · Cited by 3,408
Quantentheorie und f�nfdimensionale Relativit�tstheorie
Klein, O. (1926) · Zeitschrift f�r Physik · doi:10.1007/bf01397481 · Cited by 2,775
Quantum gravity at a Lifshitz point
Hořava, P. (2009) · Physical Review D · doi:10.1103/physrevd.79.084008 · Cited by 2,666
Self-citationDensity of states on fractals : « fractons »
Alexander, S., & Orbach, R. (1982) · Journal de Physique Lettres · doi:10.1051/jphyslet:019820043017062500 · Cited by 2,108
Heterotic and Type I string dynamics from eleven dimensions
Hořava, P., & Witten, E. (1996) · Nuclear Physics B · doi:10.1016/0550-3213(95)00621-4 · Cited by 1,984 · cited 1×
“Such extra dimensions can be of the Kaluza-Klein type [1–3], or our observed universe can be the boundary of a higher-dimensional space [4–7], or a higher codimension brane, perhaps with additional warping of the full geometry.”
BackgroundSelf-citationEleven-dimensional supergravity on a manifold with boundary
Hořava, P., & Witten, E. (1996) · Nuclear Physics B · doi:10.1016/0550-3213(96)00308-2 · Cited by 1,626
Self-citationSachdev, S. (2006) · Encyclopedia of Mathematical Physics · doi:10.1016/b0-12-512666-2/00132-2 · Cited by 1,550
Heterotic and type I string dynamics from eleven dimensions
Horava, P., & Witten, E. H. (1995) · CERN Document Server (European Organization for Nuclear Research) · Cited by 1,457
Research works printed but not linked: 4
- G. Nordström, 1914, Phys. Z., 15, 504
- 10.1016/S0920-5632(99)85202-5 · doi:10.1016/s0920-5632(99)85202-5
- 10.1088/1126-6708/1998/02/010 · doi:10.1088/1126-6708/1998/02/010
- 10.1088/0305-4470/39/5/002 · doi:10.1088/0305-4470/39/5/002
Cited by
The Confrontation between General Relativity and Experiment
Will, C. M. (2014) · Living Reviews in Relativity · doi:10.12942/lrr-2014-4 · Cited by 3,996
Barceló, C., Liberati, S., & Visser, M. (2005) · Living Reviews in Relativity · doi:10.12942/lrr-2005-12 · Cited by 1,163
de Rham, C. (2014) · Living Reviews in Relativity · doi:10.12942/lrr-2014-7 · Cited by 1,120
Barceló, C., Liberati, S., & Visser, M. (2011) · Living Reviews in Relativity · doi:10.12942/lrr-2011-3 · Cited by 598
Gravitational-Wave Tests of General Relativity with Ground-Based Detectors and Pulsar-Timing Arrays
Yunes, N., & Siemens, X. (2013) · Living Reviews in Relativity · doi:10.12942/lrr-2013-9 · Cited by 484
Metadata
- Authors
- Hořava, P.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2009-04-20
- Volume
- 102
- Issue
- 16
- Pages
- 161301-161301
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2098581578
- Cited by
- 782
- References
- 24
- FWCI
- 63.00
- Type
- journal article
- Language
- en
- Open access
- green
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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