Volume Independence in Large Nc QCD-like Gauge Theories

Journal Article · Tue Feb 06 00:00:00 EST 2007 · Journal of High Energy Physics (JHEP)

DOI:https://doi.org/10.1088/1126-6708/2007/06/019· OSTI ID:899207

Kovtun, Pavel; Unsal, Mithat; Yaffe, Laurence G

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.

• Research Organization: Stanford Linear Accelerator Center (SLAC)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC02-76SF00515
• OSTI ID: 899207
• Report Number(s): SLAC-PUB-12331; hep-th/0702021
• Journal Information: Journal of High Energy Physics (JHEP), Journal Name: Journal of High Energy Physics (JHEP)
• Country of Publication: United States
• Language: English

Related Subjects

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YANG-MILLS THEORY