Accidental Peccei-Quinn Symmetry Protected to Arbitrary Order.

@article{DiLuzio2017AccidentalPS,
  title={Accidental Peccei-Quinn Symmetry Protected to Arbitrary Order.},
  author={Luca Di Luzio and Enrico Nardi and Lorenzo Ubaldi},
  journal={Physical review letters},
  year={2017},
  volume={119 1},
  pages={
          011801
        }
}
A SU(N)_{L}×SU(N)_{R} gauge theory for a scalar multiplet Y transforming in the bifundamental representation (N,N[over ¯]) preserves, for N>4, an accidental U(1) symmetry first broken at operator dimension N. A vacuum expectation value for Y can break the symmetry to H_{s}=SU(N)_{L+R} or to H_{h}=SU(N-1)_{L}×SU(N-1)_{R}×U(1)_{L+R}. In the first case the accidental U(1) gets also broken, yielding a pseudo-Nambu-Goldstone boson with mass suppression controlled by N. In the second case a global U… 

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This point is important for the PQ solution: it ensures that the VEV of the axion will not end up canceling the SU (N )L,R θ-terms rather than θQCD

    arXiv : 1705 . 05370 . [ 21 ] Recent Developments in Gauge Theories

      Phys . Rev . Lett .

    The reader might be more familiar with the double trace Tr

      All other invariants can be expressed in terms of the set {C1(x), C2(x), . . . , CN−1(x), D}, see

        QCD asymptotic freedom is lost beyond the heavy quarks' threshold. However, Landau poles in αs remain trans-Planckian for N 26

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