Article

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; 647(5-6):515-518. 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.

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    • "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. "
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    • "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]. "
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    • "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]). "
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