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: 6.13). 04/2007; 647(5-6):515-518. DOI: 10.1016/j.physletb.2007.02.049
Source: arXiv


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.

Download full-text


Available from: Gabriele Veneziano, Jun 23, 2015
  • Source
    • "follows from charge conjugation invariance, which dictates trW † C = trW C . This last step in Yang-Mills theories does not present the conceptual issues discussed in [5] [6] for the dynamical case. The equality of the meson spectra in the three theories follows from the equality of the correlators. "
    [Show abstract] [Hide abstract]
    ABSTRACT: A numerical study of Orientifold Planar Equivalence is performed in SU(N) Yang-Mills theories for N=2,3,4,6. Quenched meson masses are extracted in the antisymmetric, symmetric and adjoint representations for the pseudoscalar and vector channels. An extrapolation of the vector mass as a function of the pseudoscalar mass to the large-N limit shows that the numerical results agree within errors for the three theories, as predicted by Orientifold Planar Equivalence. As a byproduct of the extrapolation, the size of the corrections up to O(1/N^3) are evaluated. A crucial prerequisite for the extrapolation is the determination of an analytical relationship between the corrections in the symmetric and in the antisymmetric representations, order by order in a 1/N expansion.
    Full-text · Article · Oct 2010
  • Source
    • "One is their role in technicolor theories that might be viable as extensions of the Standard Model [1] [2]. Another is the appearance of matter fields in two-index representations as components of orientifold equivalences [3] [4] [5] [6]. In connection with the first, we have been studying the lattice SU(3) gauge theory with fermions in the two-index symmetric representation, which is the sextet [7] [8]. "
    [Show abstract] [Hide abstract]
    ABSTRACT: We study the SU(3) lattice gauge theory, with two flavors of sextet Wilson-clover fermions, near its finite-temperature phase transition. We find metastable states that have Wilson line expectation values whose complex phases are near 2pi/3 or pi. The true equilibrium phase at these couplings and temperatures has its Wilson line oriented only towards the positive real axis, in agreement with perturbation theory. Comment: 14 pages, 9 figures; added a reference
    Preview · Article · Nov 2009 · Physical review D: Particles and fields
  • Source
    • "The validity of this equivalence was discussed in detail in Refs. [5] [6]. A proof of the equivalence on the lattice in the strong–coupling and large–mass phase can be found in Ref. [7] (a general – 1 – setup for descussing planar equivalences between theories with two-index representations in the strong–coupling and large–mass phase was also presented in [8] [9]). "
    [Show abstract] [Hide abstract]
    ABSTRACT: We study the center symmetry of SU(N) gauge theories with fermions in the two-index representations, by computing the effective potential of the Polyakov loop in the large-mass expansion on the lattice. In the large-N limit and at non-zero temperature, we find that the center symmetry is Z_N for fermions in the adjoint representation and just Z_2 for fermions in the (anti)symmetric representation. We discuss the fact that our results do not contradict the orientifold planar equivalence, which relates a common sector defined by the bosonic gauge-invariant C-even states of theories with fermions in different two-index representations. Our results complement the work of Armoni et al. (2007), who showed how at zero temperature a Z_N center symmetry is dynamically recovered also for fermions in the (anti)symmetric representation, by considering the theories at finite temperature.
    Preview · Article · Dec 2008 · Journal of High Energy Physics
Show more