# Dimensional reduction in manifoldlike causal sets

## Abstract

We investigate the behavior of small subsets of causal sets that approximate Minkowski space in three, four, and five dimensions, and show that their effective dimension decreases smoothly at small distances. The details of the short distance behavior depend on a choice of dimensional estimator, but for a reasonable version of the Myrheim-Meyer dimension, the minimum dimension is d ≈ 2 , reproducing results that have been seen in other approaches to quantum gravity.

- Authors:

- Univ. of California, Davis, CA (United States). Dept. of Physics

- Publication Date:

- Research Org.:
- Univ. of California, Davis, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1595490

- Alternate Identifier(s):
- OSTI ID: 1425238

- Grant/Contract Number:
- FG02-91ER40674

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 97; Journal Issue: 6; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; quantum gravity, causal sets, dimensional reduction

### Citation Formats

```
Abajian, J., and Carlip, S. Dimensional reduction in manifoldlike causal sets. United States: N. p., 2018.
Web. doi:10.1103/PhysRevD.97.066007.
```

```
Abajian, J., & Carlip, S. Dimensional reduction in manifoldlike causal sets. United States. doi:10.1103/PhysRevD.97.066007.
```

```
Abajian, J., and Carlip, S. Thu .
"Dimensional reduction in manifoldlike causal sets". United States. doi:10.1103/PhysRevD.97.066007. https://www.osti.gov/servlets/purl/1595490.
```

```
@article{osti_1595490,
```

title = {Dimensional reduction in manifoldlike causal sets},

author = {Abajian, J. and Carlip, S.},

abstractNote = {We investigate the behavior of small subsets of causal sets that approximate Minkowski space in three, four, and five dimensions, and show that their effective dimension decreases smoothly at small distances. The details of the short distance behavior depend on a choice of dimensional estimator, but for a reasonable version of the Myrheim-Meyer dimension, the minimum dimension is d ≈ 2 , reproducing results that have been seen in other approaches to quantum gravity.},

doi = {10.1103/PhysRevD.97.066007},

journal = {Physical Review D},

number = 6,

volume = 97,

place = {United States},

year = {2018},

month = {3}

}

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Works referenced in this record:

##
Fractal spacetime from the area spectrum

journal, November 2009

- Modesto, Leonardo
- Classical and Quantum Gravity, Vol. 26, Issue 24

##
Quantum spectral dimension in quantum field theory

journal, April 2016

- Calcagni, Gianluca; Modesto, Leonardo; Nardelli, Giuseppe
- International Journal of Modern Physics D, Vol. 25, Issue 05

##
Spectral dimension of a quantum universe

journal, May 2010

- Modesto, Leonardo; Nicolini, Piero
- Physical Review D, Vol. 81, Issue 10

##
The class of continuous timelike curves determines the topology of spacetime

journal, July 1977

- Malament, David B.
- Journal of Mathematical Physics, Vol. 18, Issue 7

##
Spontaneous Dimensional Reduction in Short-Distance Quantum Gravity?

conference, January 2009

- Carlip, Steven; Kowalski-Glikman, Jerzy; Durka, R.
- THE PLANCK SCALE: Proceedings of the XXV Max Born Symposium, AIP Conference Proceedings

##
Ultraviolet fixed point and generalized flow equation of quantum gravity

journal, December 2001

- Lauscher, O.; Reuter, M.
- Physical Review D, Vol. 65, Issue 2

##
What is the dimension of citation space?

journal, April 2016

- Clough, James R.; Evans, Tim S.
- Physica A: Statistical Mechanics and its Applications, Vol. 448

##
Spontaneous dimensional reduction in quantum gravity

journal, October 2016

- Carlip, S.
- International Journal of Modern Physics D, Vol. 25, Issue 12

##
Spectral dimension from nonlocal dynamics on causal sets

journal, February 2016

- Belenchia, Alessio; Benincasa, Dionigi M. T.; Marcianò, Antonino
- Physical Review D, Vol. 93, Issue 4

##
Dimension and dimensional reduction in quantum gravity

journal, September 2017

- Carlip, S.
- Classical and Quantum Gravity, Vol. 34, Issue 19

##
Echoes of asymptotic silence in causal set quantum gravity

journal, July 2017

- Eichhorn, Astrid; Mizera, Sebastian; Surya, Sumati
- Classical and Quantum Gravity, Vol. 34, Issue 16

##
Space-time as a causal set

journal, August 1987

- Bombelli, Luca; Lee, Joohan; Meyer, David
- Physical Review Letters, Vol. 59, Issue 5

##
Evidence for asymptotic safety from dimensional reduction in causal dynamical triangulations

journal, March 2015

- Coumbe, D. N.; Jurkiewicz, J.
- Journal of High Energy Physics, Vol. 2015, Issue 3

##
Spacetime with zero point length is two-dimensional at the Planck scale

journal, April 2016

- Padmanabhan, T.; Chakraborty, Sumanta; Kothawala, Dawood
- General Relativity and Gravitation, Vol. 48, Issue 5

##
The Spectral Dimension of the Universe is Scale Dependent

journal, October 2005

- Ambjørn, J.; Jurkiewicz, J.; Loll, R.
- Physical Review Letters, Vol. 95, Issue 17

##
Manifold dimension of a causal set: Tests in conformally flat spacetimes

journal, January 2003

- Reid, David D.
- Physical Review D, Vol. 67, Issue 2

##
The Hagedorn transition and the number of degrees of freedom of string theory

journal, December 1988

- Atick, Joseph J.; Witten, Edward
- Nuclear Physics B, Vol. 310, Issue 2

##
Towards a definition of locality in a manifoldlike causal set

journal, December 2013

- Glaser, Lisa; Surya, Sumati
- Physical Review D, Vol. 88, Issue 12

##
Dimensional reduction in causal set gravity

journal, November 2015

- Carlip, S.
- Classical and Quantum Gravity, Vol. 32, Issue 23

##
On the UV Dimensions of Loop Quantum Gravity

journal, January 2016

- Ronco, Michele
- Advances in High Energy Physics, Vol. 2016

##
High energy modifications of blackbody radiation and dimensional reduction

journal, July 2013

- Husain, Viqar; Seahra, Sanjeev S.; Webster, Eric J.
- Physical Review D, Vol. 88, Issue 2

##
On the ultraviolet behaviour of Newton's constant

journal, October 2004

- Percacci, Roberto; Perini, Daniele
- Classical and Quantum Gravity, Vol. 21, Issue 22

##
Lattice quantum gravity and asymptotic safety

journal, September 2017

- Laiho, J.; Bassler, S.; Coumbe, D.
- Physical Review D, Vol. 96, Issue 6

##
Super-renormalizable quantum gravity

journal, August 2012

- Modesto, Leonardo
- Physical Review D, Vol. 86, Issue 4

##
Discrete geometry of a small causal diamond

journal, February 2013

- Roy, Mriganko; Sinha, Debdeep; Surya, Sumati
- Physical Review D, Vol. 87, Issue 4

##
Discreteness Without Symmetry Breaking: a Theorem

journal, October 2009

- Bombelli, Luca; Henson, Joe; Sorkin, Rafael D.
- Modern Physics Letters A, Vol. 24, Issue 32