A note on C-parity conservation and the validity of orientifold planar equivalence

Department of Physics, Swansea University, Singleton Park, Swansea, SA2 8PP, UK
Physics Letters B (Impact Factor: 6.02). 04/2007; DOI: 10.1016/j.physletb.2007.02.049
Source: arXiv

ABSTRACT We analyze the possibility of a spontaneous breaking of C-invariance in gauge theories with fermions in vector-like—but otherwise generic—representations of the gauge group. QCD, supersymmetric Yang–Mills theory, and orientifold field theories, all belong to this class. We argue that charge conjugation is not spontaneously broken as long as Lorentz invariance is maintained. Uniqueness of the vacuum state in pure Yang–Mills theory (without fermions) and convergence of the expansion in fermion loops are key ingredients. The fact that C-invariance is conserved has an interesting application to our proof of planar equivalence between supersymmetric Yang–Mills theory and orientifold field theory on R4, since it allows the use of charge conjugation to connect the large-N limit of Wilson loops in different representations.

  • Source
    [Show abstract] [Hide abstract]
    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 orbifold-orientifold equivalence.
    Physical review D: Particles and fields 07/2007; 76(2). DOI:10.1103/PhysRevD.76.025015 · 4.86 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    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 non-zero 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 volume-reduced models in supplementing the large-volume calculations.


Available from