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We construct the most general nonlinear representation of chiral SU(2)_L xSU(2)_R broken down spontaneously to the isospin SU(2), on a pair of hadrons ofsame spin and isospin and opposite parity. We show that any such representationis equivalent, through a hadron field transformation, to two irreduciblerepresentations on two hadrons of opposite parity with different masses andaxial couplings. This implies that chiral symmetry realized in theNambu-Goldstone mode does not predict the existence of degenerate multiplets ofhadrons of opposite parity nor any relations between their couplings or masses.Comment: 4 pages, 1 figure; v3: Note added to clarify implications for hadrons  that do not couple to pions: Chiral symmetry can be realized linearly on such  states, leading to parity doubling. To the extent that they are parity  doubled, these hadrons must decouple from pions, a striking prediction that  can be tested experimentally. This applies to the work of L. Glozman and  collaborator

physical review letters

Parity Doubling and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>SU</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mi>L</mml:mi></mml:msub><mml:mo>×</mml:mo><mml:mi>SU</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mi>R</mml:mi></mml:msub></mml:math>Restoration in the Hadron Spectrum

Parity Doubling andSU(2)L×SU(2)RRestoration in the Hadron Spectrum