Volume independence in largeNcQCD-like gauge theories

Volume independence in large $\Nc$ gauge theories may be viewed as ageneralized orbifold equivalence. The reduction to zero volume (or Eguchi-Kawaireduction) is a special case of this equivalence. So is temperatureindependence in confining phases. In pure Yang-Mills theory, the failure ofvolume independence for sufficiently small volumes (at weak coupling) due tospontaneous breaking of center symmetry, together with its validity above acritical size, nicely illustrate the symmetry realization conditions which areboth necessary and sufficient for large $\Nc$ orbifold equivalence. Theexistence of a minimal size below which volume independence fails also appliesto 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 validdown to arbitrarily small size. In sufficiently large volumes, QCD(Adj) andQCD(AS) have a large $\Nc$ ``orientifold'' equivalence, provided chargeconjugation symmetry is unbroken in the latter theory. Therefore, via acombined orbifold-orientifold mapping, a well-defined large $\Nc$ equivalenceexists between QCD(AS) in large, or infinite, volume and QCD(Adj) inarbitrarily small volume. Since asymptotically free gauge theories, such asQCD(Adj), are much easier to study (analytically or numerically) in smallvolume, this equivalence should allow greater understanding of large $\Nc$ QCDin infinite volume.Comment: 32 pages, 4 figure