Spatial Modulation and Topological Current in Holographic QCD Matter

Abstract

We investigate an impact of the axial-vector interaction on spatial modulation of quark matter. A magnetic field coupled with baryon density leads to a topological axial current, so that the effect of the axial-vector interaction is crucially enhanced then. Using the Sakai-Sugimoto model we have found that, contrary to a naïve expectation, the spatially modulated phase is less favored for a stronger magnetic field, which is realized by the presence of topological current.PACS numbers: 11.25. Tq, 12.38.Mh, Introduction The phase diagram of hot and dense matter out of quarks and gluons has not been clarified satisfactorily based on the first-principle theory of the strong interaction, i.e. quantum chromodynamics (QCD). The most severe obstacle is the notorious sign problem of the Dirac determinant at finite quark density ρ or chemical potential µ, which prevents us from the direct application of the Monte-Carlo simulation in the region with µ T [1].Instead of the lattice simulation, one could have deduced possible phase structures using chiral effective models, see e.g.[2] for a recent work. It is conjectured from model studies that the chiral phase transition might be of first order at high density, so that a second-order critical point called the QCD critical point [3] could appear on the phase diagram, the discovery of which is one of the major goals of the beam-energy scan program in heavy-ion collision experiments [4]. The model setup, however, suffers from uncontrolled uncertainties and the QCD critical point is a model-dependent prediction. It is well understood by now that the vector-type interaction ∼ (ψγ µ ψ) 2 , which gives rise to the density-density interaction ∼ ρ 2 even in the mean-field level, crucially affects the liquid-gas phase transition of dense quark matter [5,6] (see also [7]). Moreover, nowadays, spatially inhomogeneous states are becoming a more and more realistic candidate that may supersede the conventional firstorder phase boundary [8], which is rather robust against the vector interaction [6, 9].The simplest Ansatz to introduce spatial modulation is the chiral spiral or the dual chiral-density wave,

Baryonic matter and beyond

“…There are not many theoretical efforts yet in this direction, probably because of uncontrollable ambiguity in model treatments. So far, there is one concrete result in the large-N c limit using the holographic QCD model [15], which suggests that the spatial modulation becomes less favored with stronger axial-vector interaction, j 5 · j 5 , that should be significantly enhanced by the topological current j 5 0. This conclusion is consistent with the observation of the p-wave pion condensate diminished by the Landau-Migdal interaction in the spin-isospin channel.…”

Spontaneous magnetization under a pseudovector interaction between quarks in high density quark matter

“…25), 26) Also, in Ref. 27), the effects of the axial-vector interaction under a strong magnetic field on the spatially-modulated chiral condensed phase was investigated by means of the holographic technique. Thus, the physics of the strong interacting matter under a magnetic field becomes interesting and important subject in quark matter with various possible phases and many investigations are carried out recently.…”

Thermodynamic phases and mesonic fluctuations in a chiral nucleon-meson model

“…Recent studies using Dyson-Schwinger equations find, in contrast, a critical endpoint of the chiral phase transition at a large critical temperature T = 100 MeV, and critical quark chemical potential in the range µ q = 170-190 MeV [23,24]. Alternative scenarios, such as the possibility of spatially inhomogeneous quark matter, are also discussed in the recent literature [25][26][27].…”