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 (2N 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(2iµzγ 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 WessZumino-Novikov-Witten model in 1 + 1 dimensions then generate strong infrared effects in 3 + 1 dimensions.

Inhomogeneous chiral condensates

“…popular but wrong definition of the quarkyonic phase as being a chirally restored but confined phase), it was realized later by Kojo, Hidaka, McLerran and Pisarski (KHMP) that the same mechanisms which lead to the DGR instability in the perturbative regime should also give rise to the emergence of CDWlike solutions in the quarkyonic phase ("quarkyonic chiral spirals", QCSs) [48]. In the following this will be discussed in more detail.…”

“…[124] the PNJL-model analysis discussed above was extended to investigate the influence of the number of colors on the phase diagram. This was motivated by the prediction of an inhomogeneous "quarkyonic" phase at large N c [48], which will be discussed in more detail in Sec. 8.…”

“…As pointed out above, the crucial step, in both, weak-coupling and the quarkyonic-matter calculations, is the reduction of the 3 + 1 dimensional problem to a 1 + 1 dimensional one, which can be done at large chemical potentials as a consequence of the collinear singularity of the gluon propagator [38,48]. In order to demonstrate the idea, consider excitations in a small patch around the point µ e z on the Fermi surface,…”

“…We see that transverse momenta are suppressed by the large chemical potential and can thus be neglected in leading order. Assuming that this remains true for the dressed propagator S(k) (which can be justified a posteriori), we can use this to evaluate the quark selfenergy [48] Σ…”

“…It is therefore difficult for them to form a collective state, since the gluon propagator is suppressed at large momenta. [48].…”