Chiral symmetry restoration at finite density in largeNcQCD

Abstract

At large Nc, 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 non-linear 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 Nc 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. It is also shown that this no-go theorem is fully consistent with the vanishing of the spatial average of the chiral condensate 1 2 Tr(U) (as happens in "half-skyrmion" configurations). This is because the chiral condensate is only one of an infinite set of chiral order parameters, some of which must be non-zero. It is also shown that while an approximation of a unit cell of a Skyrme crystal as a hypersphere does lead to a phase which is chirally restored (in the average sense), this is an artifact of the approximation.

Heavy-tailed chiral random matrix theory

“…Secondly, in phases with spatially modulated chiral condensates, the phonon fluctuations associated with translational symmetry breaking wipe out the spatial order and lead to a phase with quartic condensates [44]. Other related arguments can be found in [45][46][47][48][49][50].…”

Chiral symmetry restoration in static-light mesons: A chiral restoration theorem, the quark running mass m(k) , and chiral restoration signals in the lattice QCD spectra

“…In what concerns large density, new chiral phases are expected but they have not yet been observed yet [5][6][7]. Chiral symmetry restoration is also important for the modifications of the hadron spectrum in nuclear matter [8,9].…”

Chiral symmetry breaking with no bilinear condensate revisited

“…Indeed, a Ginzburg-Landau-type analysis in a chiral effective model suggests that this is likely to be the case [9]. In addition, studies of inhomogeneous chirally broken phases in dense QCD suggest that chiral symmetry breaking in such phases could be driven not by the chiral condensate but rather by a higherorder condensate [10,11]: the basic idea of [11] is that a one-dimensionally modulated chiral condensate is wiped out by thermal fluctuations of phonons, whereas [10] shows in QCD at large N that a higher-order chiral order parameter whose spatial average is nonzero must exist when the chiral condensate is locally nonzero but its spatial average vanishes. Recently, phases with massive fermions with no bilinear condensate have been found in numerical simulations [12,13], which bears resemblance to the Stern phase.…”