Quarkyonic chiral spirals

Abstract

We consider the formation of chiral density waves in Quarkyonic matter, which is a phase where cold, dense quarks experience confining forces. We model confinement following Gribov and Zwanziger, taking the gluon propagator, in Coulomb gauge and momentum space, as ∼ 1 / ( p → 2 ) 2 . We assume that the number of colors, N c , is large, and that the quark chemical potential, μ, is much larger than renormalization mass scale, Λ QCD . To leading order in 1 / N c and Λ QCD / μ , a gauge theory with N f flavors of massless quarks in 3 + 1 dimensions naturally reduces to a gauge theory in 1 + 1 dimensions, with an enlarged flavor symmetry of SU ( 2 N f ) . Through an anomalous chiral rotation, in two dimensions a Fermi sea of massless quarks maps directly onto the corresponding theory in vacuum. A chiral condensate forms locally, and varies with the spatial position, z, as 〈 ψ ¯ exp ( 2 i μ z γ 0 γ z ) ψ 〉 . Following Schön and Thies, we term this two-dimensional pion condensate a (Quarkyonic) chiral spiral. Massive quarks also exhibit chiral spirals, with the magnitude of the oscillations decreasing smoothly with increasing mass. The power law correlations of the Wess–Zumino–Novikov–Witten model in 1 + 1 dimensions then generate strong infrared effects in 3 + 1 dimensions.