On Chiral Symmetry Restoration at Finite Density in Large N_c QCD

Abstract

At large N_c, cold nuclear matter is expected to form a crystal and thus spontaneously break translational symmetry. The description of chiral symmetry breaking and translational symmetry breaking can become intertwined. Here, the focus is on aspects of chiral symmetry breaking and its possible restoration that are by construction independent of the nature of translational symmetry breaking---namely spatial averages of chiral order parameters. A system will be considered to be chirally restored provided all spatially-averaged chiral order parameters are zero. A critical question is whether chiral restoration in this sense is possible for phases in which chiral order parameters are locally non-zero but whose spatial averages all vanish. We show that this is not possible unless all chirally-invariant observables are spatially uniform. This result is first derived for Skyrme-type models, which are based on a nonlinear sigma model and by construction break chiral symmetry on a point-by-point basis. A no-go theorem for chiral restoration (in the average sense) for all models of this type is obtained by showing that in these models there exist chirally symmetric order parameters which cannot be spatially uniform. Next we show that the no-go theorem applies to large N_c QCD in any phase which has a non-zero but spatially varying chiral condensate. The theorem is demonstrated by showing that in a putative chirally-restored phase, the field configuration can be reduced to that of a nonlinear sigma model.

arXiv comment12 pages, 1 table

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Cited by in corpus (6)

• No-Go Theorem for Critical Phenomena in Large-Nc QCD
• A pseudo-conformal structure in dense baryonic matter
• Sign problem and phase quenching in finite-density QCD: models, holography, and lattice
• Chiral symmetry breaking with no bilinear condensate revisited
• Chiral symmetry restoration in static-light mesons: chiral restoration theorem, the quark running mass m(k) and first chiral restoration signals in the lattice QCD spectra
• Comment on chiral symmetry restoration at finite density in large-$N_c$ QCD