Article
A note on Cparity conservation and the validity of orientifold planar equivalence
Department of Physics, Swansea University, Singleton Park, Swansea, SA2 8PP, UK; William I. Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, MN 55455, USA; Theory Division, CERN CH1211 Geneva 23, Switzerland; Collège de France, 11 place M. Berthelot, 75005 Paris, France
Physics Letters B (Impact Factor: 4.57). 01/2007; DOI: 10.1016/j.physletb.2007.02.049 Source: arXiv

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ABSTRACT: This work covers volume reduction in quantum field theories on a lattice at large $N$ (number of colors), as first described by Eguchi and Kawai in 1982. The volume reduction (or volume independence) means that the theory defined on an arbitrarily small lattice is equivalent in the large$N$ limit to the theory on an infinite lattice with the same bare parameters. We analyze the volume reduction by means of Monte Carlo simulations using the lattice model on a single site (or a small fixed number of sites) with Wilson fermions in the adjoint representation, using $N$ up to 60. Most of the results focus on two flavours of Dirac fermions and the single fermionic flavour is also discussed where there is a significant difference of behaviour. We find that the $(Z_N)^4$ center symmetry, necessary for the realization of volume reduction, is unbroken in the reduced model for a large range of parameters and, in particular, that the maximum admissible value of the adjoint fermion mass is nonzero in the large$N$ limit. We calculate physical quantities, such as the plaquette, the static quark potential and the eigenvalues of the Dirac operator. We analyze the finite$N$ corrections and consider the practicality of volumereduced models in supplementing the largevolume calculations.12/2013; 
Article: Phases of N=∞ QCDlike gauge theories on S3×S1 and nonperturbative orbifoldorientifold equivalences
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ABSTRACT: We study the phase diagrams of N=∞ vectorlike, asymptotically free gauge theories as a function of volume, on S3×S1. The theories of interest are the ones with fermions in two index representations [adjoint, (anti)symmetric, and bifundamental abbreviated as QCD(adj), QCD(AS/S), and QCD(BF)], and are interrelated via orbifold or orientifold projections. The phase diagrams reveal interesting phenomena such as disentangled realizations of chiral and center symmetry, confinement without chiral symmetry breaking, zero temperature chiral transitions, and in some cases, exotic phases which spontaneously break the discrete symmetries such as C, P, T as well as CPT. In a regime where the theories are perturbative, the deconfinement temperature in SYM, and QCD(AS/S/BF) coincide. The thermal phase diagrams of thermal orbifold QCD(BF), orientifold QCD(AS/S), and N=1 SYM coincide, provided charge conjugation symmetry for QCD(AS/S) and Z2 interchange symmetry of the QCD(BF) are not broken in the phase continuously connected to the R4 limit. When the S1 circle is endowed with periodic boundary conditions, the (nonthermal) phase diagrams of orbifold and orientifold QCD are still the same, however, both theories possess chirally symmetric phases which are absent in N=1 SYM. The match and mismatch of the phase diagrams depending on the spin structure of fermions along the S1 circle is naturally explained in terms of the necessary and sufficient symmetry realization conditions which determine the validity of the nonperturbative orbifoldorientifold equivalence.Physical review D: Particles and fields 01/2007; 76(2).
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