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An alternative pattern of the chiral symmetry breaking, suggested recently byStern, 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 $Z_{N_f}$ thenwould play a custodial role preventing the quark bilinears from condensation.It is shown that this pattern of the chiral symmetry breaking is ruled out inQCD by exact inequalities. It is not ruled out, however, in other gaugetheories with scalar quarks and/or Yukawa couplings.Comment: 9 pages, Latex, clarifying comments and several references adde

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Chiral symmetry breaking without bilinear condensates, unbroken axial<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>Z</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>symmetry, and exact QCD inequalities

Chiral symmetry breaking without bilinear condensates, unbroken axialZNsymmetry, and exact QCD inequalities