Phases of rotating baryonic matter: non-Abelian chiral soliton lattices, antiferro-isospin chains, and ferri/ferromagnetic magnetization

Abstract

A chiral soliton lattice (CSL), proposed as the ground state of rotating baryonic matter at a finite density, is shown to be unstable in a large parameter region for two flavors owing to pion condensations, leading to two types of non-Abelian (NA) CSL phases (dimer and deconfining phases). We determine the phase diagram where the dimer phase meets the other phases and QCD vacuum at three tricritical points. The critical angular velocity of NA-CSLs is lower than that of η-CSL. Each NA soliton carries an isospin, and an antiferro-isospin chain is formed leading to gapless isospinons. The anomalous coupling to the magnetic field makes the NA-CSL (η-CSL) ferrimagnetic (ferromagnetic).

Chiral soliton lattice at next-to-leading order

“…Finally, note that the original prediction of the CSL phase in QCD under strong magnetic fields [1] was subsequently extended to related setups where either the external conditions or the dynamical theory itself may differ. This applies in particular to dense QCD matter under uniform rotation in presence of a baryon or isospin chemical potential or both [34][35][36], QCD in external magnetic field and with nonzero isospin chemical potential [37,38], and a class of QCD-like theories with nonzero magnetic field and baryon chemical potential [39,40]. We expect the computational techniques developed here to be useful also in these other contexts, should one be interested in the effects of quantum or thermal fluctuations therein.…”

Domain-wall Skyrmion phase in a rapidly rotating QCD matter

“…In the case of ϵ < 0 denoted by the blue shaded region in figure 2, the CSL is the Abelian confined CSL. The critical angular velocity in the Abelian CSL is known to be S = 4/π [12,53]. In the case of ϵ = 0 denoted by the green line in figure 2, the up and down solitons do not interact, and they form lattices independently.…”

“…moduli as a consequence of the spontaneous breaking of the vector symmetry SU(2) V in the vicinity of each soliton [53]. In such a non-Abelian CSL, we have shown that the effective world-volume theory of a single non-Abelian soliton is a d = 2 + 1 dimensional CP 1 model [O(3) model] with a topological term originated from the WZW term, eq.…”

“…Quark-gluon plasmas produced in non-central heavy-ion collision experiments at the Relativistic Heavy Ion Collider (RHIC) reach the largest vorticity observed thus far, of the order of 10 22 /s [37,38]. This has triggered significant attention to rotating QCD matter in recent years [39][40][41][42][43][44][45][46][47][48][49][50][51][52][53]. In particular, similar but different type of CSL appears in QCD at finite density under rapid rotation instead of a strong magnetic field.…”

“…However, it was shown in ref. [53] that in a large parameter region, a single η-soliton energetically decays into a pair of non-Abelian solitons, around which the neutral pion condensation occurs. A single non-Abelian soliton spontaneously breaks the vector symmetry SU(2) V into its U(1) subgroup, resulting in NG modes SU(2) V /U(1) ≃ CP 1 ≃ S 2 localized in the vicinity of the soliton.…”