Volume Independence in Large Nc QCDlike 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 EguchiKawai 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 YangMills 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 YangMills theory with antisymmetric representation fermions [QCD(AS)]. However, in YangMills 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 orbifoldorientifold mapping, a welldefined 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):
 SLACPUB12331
hepth/0702021; TRN: US0701928
 DOE Contract Number:
 AC0276SF00515
 Resource Type:
 Journal Article
 Resource Relation:
 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; YANGMILLS THEORY; TheoryHEP,HEPTH
Citation Formats
Kovtun, Pavel, Unsal, Mithat, and Yaffe, Laurence G. Volume Independence in Large Nc QCDlike Gauge Theories. United States: N. p., 2007.
Web. doi:10.1088/11266708/2007/06/019.
Kovtun, Pavel, Unsal, Mithat, & Yaffe, Laurence G. Volume Independence in Large Nc QCDlike Gauge Theories. United States. doi:10.1088/11266708/2007/06/019.
Kovtun, Pavel, Unsal, Mithat, and Yaffe, Laurence G. Tue .
"Volume Independence in Large Nc QCDlike Gauge Theories". United States.
doi:10.1088/11266708/2007/06/019. https://www.osti.gov/servlets/purl/899207.
@article{osti_899207,
title = {Volume Independence in Large Nc QCDlike 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 EguchiKawai 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 YangMills 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 YangMills theory with antisymmetric representation fermions [QCD(AS)]. However, in YangMills 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 orbifoldorientifold mapping, a welldefined 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 = {10.1088/11266708/2007/06/019},
journal = {Journal of High Energy Physics (JHEP)},
number = ,
volume = ,
place = {United States},
year = {Tue Feb 06 00:00:00 EST 2007},
month = {Tue Feb 06 00:00:00 EST 2007}
}

Consequences of large N volume independence are examined in conformal and confining gauge theories. In the large N limit, gauge theories compactified on R{sup dk} x (S{sup 1}){sup k} are independent of the S{sup 1} radii, provided the theory has unbroken center symmetry. In particular, this implies that a large N gauge theory which, on R{sup d}, flows to an IR fixed point, retains the infinite correlation length and other scale invariant properties of the decompactified theory even when compactified on R{sup dk} x (S{sup 1}){sup k}. In other words, finite volume effects are 1/N suppressed. In lattice formulations ofmore »

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