# Quantum gravity in large dimensions

## Abstract

Quantum gravity is investigated in the limit of a large number of space-time dimensions d, using as an ultraviolet regularization the simplicial lattice path integral formulation. In the weak field limit the appropriate expansion parameter is determined to be 1/d. For the case of a simplicial lattice dual to a hypercube, the critical point is found at k{sub c}/{lambda}=1/d (with k=1/8{pi}G) separating a weak coupling from a strong coupling phase, and with 2d{sup 2} degenerate zero modes at k{sub c}. The strong coupling, large G, phase is then investigated by analyzing the general structure of the strong coupling expansion in the large d limit. Dominant contributions to the curvature correlation functions are described by large closed random polygonal surfaces, for which excluded volume effects can be neglected at large d, and whose geometry we argue can be approximated by unconstrained random surfaces in this limit. In large dimensions the gravitational correlation length is then found to behave as vertical bar log(k{sub c}-k) vertical bar{sup 1/2}, implying for the universal gravitational critical exponent the value {nu}=0 at d={infinity}.

- Authors:

- Department of Physics and Astronomy, University of California, Irvine, California 92697-4575 (United States)
- (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 20776769

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.73.044031; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CORRELATION FUNCTIONS; CORRELATIONS; COUPLING; GEOMETRY; PATH INTEGRALS; QUANTUM GRAVITY; RANDOMNESS; SPACE-TIME; STRONG-COUPLING MODEL; ULTRAVIOLET RADIATION

### Citation Formats

```
Hamber, Herbert W., Williams, Ruth M., Girton College, Cambridge CB3 0JG, and and Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA.
```*Quantum gravity in large dimensions*. United States: N. p., 2006.
Web. doi:10.1103/PhysRevD.73.044031.

```
Hamber, Herbert W., Williams, Ruth M., Girton College, Cambridge CB3 0JG, & and Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA.
```*Quantum gravity in large dimensions*. United States. doi:10.1103/PhysRevD.73.044031.

```
Hamber, Herbert W., Williams, Ruth M., Girton College, Cambridge CB3 0JG, and and Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA. Wed .
"Quantum gravity in large dimensions". United States.
doi:10.1103/PhysRevD.73.044031.
```

```
@article{osti_20776769,
```

title = {Quantum gravity in large dimensions},

author = {Hamber, Herbert W. and Williams, Ruth M. and Girton College, Cambridge CB3 0JG and and Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA},

abstractNote = {Quantum gravity is investigated in the limit of a large number of space-time dimensions d, using as an ultraviolet regularization the simplicial lattice path integral formulation. In the weak field limit the appropriate expansion parameter is determined to be 1/d. For the case of a simplicial lattice dual to a hypercube, the critical point is found at k{sub c}/{lambda}=1/d (with k=1/8{pi}G) separating a weak coupling from a strong coupling phase, and with 2d{sup 2} degenerate zero modes at k{sub c}. The strong coupling, large G, phase is then investigated by analyzing the general structure of the strong coupling expansion in the large d limit. Dominant contributions to the curvature correlation functions are described by large closed random polygonal surfaces, for which excluded volume effects can be neglected at large d, and whose geometry we argue can be approximated by unconstrained random surfaces in this limit. In large dimensions the gravitational correlation length is then found to behave as vertical bar log(k{sub c}-k) vertical bar{sup 1/2}, implying for the universal gravitational critical exponent the value {nu}=0 at d={infinity}.},

doi = {10.1103/PhysRevD.73.044031},

journal = {Physical Review. D, Particles Fields},

number = 4,

volume = 73,

place = {United States},

year = {Wed Feb 15 00:00:00 EST 2006},

month = {Wed Feb 15 00:00:00 EST 2006}

}