Toru Kojo

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 Schon 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.

The quark mass gap in a magnetic field

A magnetic eld and the resulting Landau degeneracy enhance the infrared contributions to the quark mass gap. The gap does not grow arbitrarily, however, for models of asymptotic free interactions. For B ! 1, the magnetic eld decouples from the dimensionally reduced selfconsistent equations, so that the gap behaves as QCD (or less), instead of p jeBj. On the other hand, the number of participants to the chiral condensate keeps increasing asj eBj so that jh ij j eBj QCD. After the mass gap stops developing, nothing tempers the growth of screening eects as B! 1. These features are utilized to interpret the reduction of critical temperatures for the chiral and deconnement phase transitions at nite B, recently found on the lattice. The structures of mesons are analyzed and light mesons are identied. Applications for cold, dense quark matter are also briey discussed.

Interweaving chiral spirals

Abstract We elaborate how to construct interweaving chiral spirals in ( 2 + 1 ) dimensions, defined as a superposition of chiral spirals oriented in different directions. We divide a two-dimensional Fermi sea into distinct wedges, characterized by the opening angle 2 Θ and depth Q ≃ p F , where p F is the Fermi momentum. In each wedge, the energy is lowered by forming a single chiral spiral. The optimal values for Θ and Q are chosen by balancing this gain in energy versus the cost of deforming the Fermi surface (which dominates at large Θ ) and patch–patch interactions (dominant at small Θ ). Using a non-local four-Fermi interaction model, we estimate the gain and cost in energy by expanding in terms of 1 / N c (where N c is the number of colors), Λ QCD / Q , and Θ . Due to a form factor in our non-local model, at small 1 / N c the mass gap (chiral condensate) is large, and the interaction among quarks and the condensate local in momentum space. Consequently, interactions between different patches are localized near their boundaries, and it is simple to embed many chiral spirals. We identify the dominant and subdominant terms at high density and categorize formulate an expansion in terms of Λ QCD / Q or Θ . The kinetic term in the transverse directions is subdominant, so that techniques from ( 1 + 1 ) -dimensional systems can be utilized. To leading order in 1 / N c and Λ QCD / Q , the total gain in energy is ∼ p F Λ QCD 2 with Θ ∼ ( Λ QCD / p F ) 3 / 5 . Since Θ decreases with increasing p F , there should be phase transitions associated with the change in the wedge number. We also argue the effects of subdominant terms at lower density where the large- N c approximation is more reliable.

Covering the Fermi surface with patches of quarkyonic chiral spirals

We argue that in cold, dense quark matter, in the limit of a large number of colors the ground state is unstable with respect to creation of a complicated quarkyonic chiral spiral state, in which both chiral and translational symmetries are spontaneously broken. The entire Fermi surface is covered with patches of quarkyonic chiral spirals, whose number increases as the quark density does. The low energy excitations are gapless, given by the Wess-Zumino-Novikov-Witten model plus transverse kinetic terms localized about different patches.

The Quarkyonic Star

We discuss theoretical scenarios on crossover between nuclear matter (NM) and quark matter (QM). We classify various possibilities into three major scenarios according to the onset of diquark degrees of freedom that characterizes color-superconducting (CSC) states. In the conventional scenario NM occurs at the liquid-gas (or liquid-vacuum at zero temperature) phase transition and QM occurs next, after which CSC eventually appears. With the effect of strong correlation, the BEC-BCS scenario implies that CSC occurs next to NM and QM comes last in the BCS regime. We adopt the quarkyonic scenario in which NM, QM, and CSC are theoretically indistinguishable and thus these names refer to not distinct states but relevant descriptions of the same physical system. Based on this idea we propose a natural scheme to interpolate NM near normal nuclear density and CSC with vector coupling at high baryon density. We finally discuss the mass-radius relation of the neutron star and constraints on parameters in the proposed scheme.

A (1+1)-dimensional example of Quarkyonic matter

Abstract We analyze the ( 1 + 1 )-dimensional QCD (QCD2) at finite density to consider a number of qualitative issues: confinement in dense quark matter, the chiral symmetry breaking near the Fermi surface, the relation between chiral spirals and quark number density, and a possibility of the spontaneous flavor symmetry breaking. We argue that while the free energy is dominated by perturbative quarks, confined excitations at zero density can persist up to high density. So quark matter in QCD2 is an example of Quarkyonic matter. The non-Abelian bosonization and associated charge–flavor–color separation are mainly used in order to clarify basic structures of QCD2 at finite density.

Phenomenological neutron star equations of state - 3-window modeling of QCD matter

Abstract.We discuss the 3-window modeling of cold, dense QCD matter equations of state at density relevant to neutron star properties. At low baryon density,

A renormalization group approach for QCD in a strong magnetic field

n_{B}\lesssim 2n_{s}

The Dichotomous Nucleon: Some Radical Conjectures for the Large Nc Limit

(

Phenomenological QCD equations of state for neutron stars

n_{s}