# 5-D Choptuik critical exponent and holography

## Abstract

Recently, a holographic argument was used to relate the saturation exponent, {gamma}{sub BFKL}, of 4-dimensional Yang-Mills theory in the Regge limit to the Choptuik critical scaling exponent, {gamma}{sub 5d}, in 5-dimensional black hole formation via scalar field collapse [L. Alvarez-Gaume, C. Gomez, and M. A. Vazquez-Mozo, arXiv:hep-th/0611312.]. Remarkably, the numerical value of the former agreed quite well with previous calculations of the latter. We present new results of an improved calculation of {gamma}{sub 5d} with substantially decreased numerical error. Our current result is {gamma}{sub 5d}=0.4131{+-}0.0001, which is close to, but not in strict agreement with, the value of {gamma}{sub BFKL}=0.409 552 quoted in [L. Alvarez-Gaume, C. Gomez, and M. A. Vazquez-Mozo, arXiv:hep-th/0611312.].

- Authors:

- Department of Physics and Astronomy and Winnipeg Institute of Theoretical Physics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2 (Canada)
- Department of Physics and Winnipeg Institute of Theoretical Physics, University of Winnipeg, Winnipeg, Manitoba, R3B 2E9 (Canada)

- Publication Date:

- OSTI Identifier:
- 20935241

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.75.101501; (c) 2007 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; BLACK HOLES; COSMOLOGICAL MODELS; ERRORS; HOLOGRAPHY; MANY-DIMENSIONAL CALCULATIONS; SCALAR FIELDS; YANG-MILLS THEORY

### Citation Formats

```
Bland, J., and Kunstatter, G.
```*5-D Choptuik critical exponent and holography*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.101501.

```
Bland, J., & Kunstatter, G.
```*5-D Choptuik critical exponent and holography*. United States. doi:10.1103/PHYSREVD.75.101501.

```
Bland, J., and Kunstatter, G. Tue .
"5-D Choptuik critical exponent and holography". United States.
doi:10.1103/PHYSREVD.75.101501.
```

```
@article{osti_20935241,
```

title = {5-D Choptuik critical exponent and holography},

author = {Bland, J. and Kunstatter, G.},

abstractNote = {Recently, a holographic argument was used to relate the saturation exponent, {gamma}{sub BFKL}, of 4-dimensional Yang-Mills theory in the Regge limit to the Choptuik critical scaling exponent, {gamma}{sub 5d}, in 5-dimensional black hole formation via scalar field collapse [L. Alvarez-Gaume, C. Gomez, and M. A. Vazquez-Mozo, arXiv:hep-th/0611312.]. Remarkably, the numerical value of the former agreed quite well with previous calculations of the latter. We present new results of an improved calculation of {gamma}{sub 5d} with substantially decreased numerical error. Our current result is {gamma}{sub 5d}=0.4131{+-}0.0001, which is close to, but not in strict agreement with, the value of {gamma}{sub BFKL}=0.409 552 quoted in [L. Alvarez-Gaume, C. Gomez, and M. A. Vazquez-Mozo, arXiv:hep-th/0611312.].},

doi = {10.1103/PHYSREVD.75.101501},

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

number = 10,

volume = 75,

place = {United States},

year = {Tue May 15 00:00:00 EDT 2007},

month = {Tue May 15 00:00:00 EDT 2007}

}