# Volume Independence in Large Nc QCD-like Gauge Theories

## Abstract

Volume independence in large N{sub c} gauge theories may be viewed as a generalized orbifold equivalence. The reduction to zero volume (or Eguchi-Kawai reduction) is a special case of this equivalence. So is temperature independence in confining phases. A natural generalization concerns volume independence in ''theory space'' of quiver gauge theories. In pure Yang-Mills theory, the failure of volume independence for sufficiently small volumes (at weak coupling) due to spontaneous breaking of center symmetry, together with its validity above a critical size, nicely illustrate the symmetry realization conditions which are both necessary and sufficient for large N{sub c} orbifold equivalence. The existence of a minimal size below which volume independence fails also applies to Yang-Mills theory with antisymmetric representation fermions [QCD(AS)]. However, in Yang-Mills theory with adjoint representation fermions [QCD(Adj)], endowed with periodic boundary conditions, volume independence remains valid down to arbitrarily small size. In sufficiently large volumes, QCD(Adj) and QCD(AS) have a large N{sub c} ''orientifold'' equivalence, provided charge conjugation symmetry is unbroken in the latter theory. Therefore, via a combined orbifold-orientifold mapping, a well-defined large N{sub c} equivalence exists between QCD(AS) in large, or infinite, volume and QCD(Adj) in arbitrarily small volume. Since asymptotically free gauge theories, suchmore »

- Authors:

- Publication Date:

- Research Org.:
- Stanford Linear Accelerator Center (SLAC)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 899207

- Report Number(s):
- SLAC-PUB-12331

hep-th/0702021; TRN: US0701928

- DOE Contract Number:
- AC02-76SF00515

- Resource Type:
- Journal Article

- Journal Name:
- Journal of High Energy Physics (JHEP)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (JHEP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUNDARY CONDITIONS; CRITICAL SIZE; FERMIONS; QUANTUM CHROMODYNAMICS; SYMMETRY; YANG-MILLS THEORY; Theory-HEP,HEPTH

### Citation Formats

```
Kovtun, Pavel, Unsal, Mithat, and Yaffe, Laurence G.
```*Volume Independence in Large Nc QCD-like Gauge Theories*. United States: N. p., 2007.
Web. doi:10.1088/1126-6708/2007/06/019.

```
Kovtun, Pavel, Unsal, Mithat, & Yaffe, Laurence G.
```*Volume Independence in Large Nc QCD-like Gauge Theories*. United States. https://doi.org/10.1088/1126-6708/2007/06/019

```
Kovtun, Pavel, Unsal, Mithat, and Yaffe, Laurence G. Tue .
"Volume Independence in Large Nc QCD-like Gauge Theories". United States. https://doi.org/10.1088/1126-6708/2007/06/019. https://www.osti.gov/servlets/purl/899207.
```

```
@article{osti_899207,
```

title = {Volume Independence in Large Nc QCD-like Gauge Theories},

author = {Kovtun, Pavel and Unsal, Mithat and Yaffe, Laurence G},

abstractNote = {Volume independence in large N{sub c} gauge theories may be viewed as a generalized orbifold equivalence. The reduction to zero volume (or Eguchi-Kawai reduction) is a special case of this equivalence. So is temperature independence in confining phases. A natural generalization concerns volume independence in ''theory space'' of quiver gauge theories. In pure Yang-Mills theory, the failure of volume independence for sufficiently small volumes (at weak coupling) due to spontaneous breaking of center symmetry, together with its validity above a critical size, nicely illustrate the symmetry realization conditions which are both necessary and sufficient for large N{sub c} orbifold equivalence. The existence of a minimal size below which volume independence fails also applies to Yang-Mills theory with antisymmetric representation fermions [QCD(AS)]. However, in Yang-Mills theory with adjoint representation fermions [QCD(Adj)], endowed with periodic boundary conditions, volume independence remains valid down to arbitrarily small size. In sufficiently large volumes, QCD(Adj) and QCD(AS) have a large N{sub c} ''orientifold'' equivalence, provided charge conjugation symmetry is unbroken in the latter theory. Therefore, via a combined orbifold-orientifold mapping, a well-defined large N{sub c} equivalence exists between QCD(AS) in large, or infinite, volume and QCD(Adj) in arbitrarily small volume. Since asymptotically free gauge theories, such as QCD(Adj), are much easier to study (analytically or numerically) in small volume, this equivalence should allow greater understanding of large N{sub c} QCD in infinite volume.},

doi = {10.1088/1126-6708/2007/06/019},

url = {https://www.osti.gov/biblio/899207},
journal = {Journal of High Energy Physics (JHEP)},

number = ,

volume = ,

place = {United States},

year = {2007},

month = {2}

}