Inhomogeneous Chiral Phase in Quark Matter

Abstract

Recent development of inhomogeneous chiral phase in Kyoto group is briefly reviewed. First, the nesting effect of the Fermi surface is emphasized as a key mechanism leading to inhomogeneous chiral phase. After introduction of inhomogeneous chiral phase, some topological aspects are discussed in 1+1 dimensions and in the presence of the magnetic field in 1+3 dimensions. Spectral asymmetry gives rise to anomalous quark number and is closely related to chiral anomaly. It may induce spontaneous magnetization and a novel Lifshitz point may appear on the zero chemical potential line, µ = 0. Some astronomical implications are briefly discussed. Finally, the effects of the fluctuations around the order parameter are discussed; the propagator of the fluctuations exhibits a singularity at finite momentum and changes the properties of the phase transition through loop diagrams.

Transport Properties in Dense QCD Matter

“…Many studies have shown that the chiral transition from the spontaneously symmetry-broken (SSB) phase to the quark-gluon plasma (QGP) phase should be present at some density and temperature, using the effective models of QCD, while at the moment it has not yet been directly proven from the first principle computations with lattice gauge theory due to the sign problem [2]. Recently, the possible appearance of the inhomogeneous chiral phase (iCP) has been suggested near the chiral transition, and extensively studied in various situations, including in the presence of magnetic field [3][4][5][6][7][8].…”

“…We, hereafter, focus on this type, because the phase degree of freedom is indispensable for manifestation of topological effects in iCP. Moreover, it may be the most favorable configuration in the presence of the magnetic field [6][7][8].…”

“…with E p = p 2 + M 2 for each flavor, where ε and s denote the particle-antiparticle and spin degrees of freedom, respectively. Accordingly, this form suggests anisotropy of the Fermi sea in the momentum space: it deforms in an axial-symmetric way around the direction of q. Thermodynamic potential can be easily evaluated for given temperature T and baryon number chemical potential µ, using the single-particle energy (7). Then, the values of the order parameters can be easily extracted: we can see that the DCDW phase appears around several times the normal nuclear density at T = 0 (see Figure 1a), where the usual chiral transition has been expected [3].…”