Chiral Symmetry Breaking without Bilinear Condensates, Unbroken Axial Z_N Symmetry, and Exact QCD Inequalities

Abstract

An alternative pattern of the chiral symmetry breaking, suggested recently by Stern, is investigated. It could be self-consistent provided that the chiral $SU(N_f)\times SU(N_f)$ symmetry is broken spontaneously down to $SU(N_f)\times Z_{N_f}$ rather than to $SU(N_f{)}_V$. The discrete axial $Z_{N_f}$ then would play a custodial role preventing the quark bilinears from condensation. It is shown that this pattern of the chiral symmetry breaking is ruled out in QCD by exact inequalities. It is not ruled out, however, in other gauge theories with scalar quarks and/or Yukawa couplings.

9 pages, Latex, clarifying comments and several references added

References in corpus (3)

• QCD at Finite Baryon Density: Nucleon Droplets and Color Superconductivity
• Diquark Bose Condensates in High Density Matter and Instantons
• Patterns of Spontaneous Chiral Symmetry Breaking in the Large-Nc Limit of QCD-Like Theories

Cited by in corpus (34)

• The phase diagram of dense QCD
• Inverse meson mass ordering in color-flavor-locking phase of high density QCD
• Hadron properties in the nuclear medium
• Patterns of Symmetry Breaking in QCD at High Baryon Density
• Recent Progress in QCD Condensate Evaluations and Sum Rules
• Anomaly matching for phase diagram of massless ${\mathbb{Z}}_N$-QCD
• Novel phase in SU(3) lattice gauge theory with 12 light fermions
• Anomaly constraint on massless QCD and the role of Skyrmions in chiral symmetry breaking
• Paramagnetic effect of light quark loops on Chiral Symmetry Breaking
• Scale-Invariant Hidden Local Symmetry, Topology Change and Dense Baryonic Matter II
• Massive fermions without fermion bilinear condensates
• Parity doubling in particle physics
• Parity Doubling Among the Baryons
• Fractional $\theta$ angle, 't Hooft anomaly, and quantum instantons in charge-$q$ multi-flavor Schwinger model
• Fermion masses through four-fermion condensates
• Dense baryonic matter in conformally-compensated hidden local symmetry: Vector manifestation and chiral symmetry restoration
• Excited Scalar and Pseudoscalar Mesons in the Extended Linear Sigma Model
• Scale-Invariant Hidden Local Symmetry, Topology Change and Dense Baryonic Matter
• 't Hooft anomaly matching condition and chiral symmetry breaking without bilinear condensate
• Chiral order and fluctuations in multi-flavour QCD
• Non-perturbative analysis of the spectrum of meson resonances in an ultraviolet-complete composite-Higgs model
• Enhancement of quark number susceptibility with an alternative pattern of chiral symmetry breaking in dense matter
• Quark description of the Nambu-Goldstone bosons in the color-flavor locked phase
• Chiral symmetry breaking with no bilinear condensate revisited
• Low-energy photon-photon fusion into three pions in Generalized Chiral Perturbation Theory
• The World as a Dual Josephson Junction
• How tetraquarks can generate a second chiral phase transition
• Eta' Mass and Chiral Symmetry Breaking at Large Nc and Nf
• Finite-volume analysis of N_f-induced chiral phase transitions
• Poincare covariant pseudoscalar and scalar meson spectroscopy in Wigner-Weyl phase
• On Chiral Symmetry Restoration at Finite Density in Large N_c QCD
• Chiral random matrix theory for colorful quark-antiquark condensates
• Nonrelativistic Banks-Casher relation and random matrix theory for multi-component fermionic superfluids
• Fermion Bags and A New Origin for a Fermion Mass