Abstract
We study the ground states of low-density hadronic matter and high-density color-flavor locked color superconducting phase in three-flavor QCD at finite baryon chemical potential under rotation. We find that, in both cases under sufficiently fast rotation, the combination of the rotation-induced topological term for the η′ meson and the QCD anomaly leads to an inhomogeneous condensate of the η′ meson, known as the chiral soliton lattice (CSL). We find that, when baryon chemical potential is much larger than isospin chemical potential, the critical angular velocity for the realization of the η′ CSL is much smaller than that for the π0 CSL found previously. We also argue that the η′ CSL states in flavor-symmetric QCD at low density and high density should be continuously connected, extending the quark-hadron continuity conjecture in the presence of the rotation.
Highlights
Total derivative term DM interaction D · ∇φ WZW-type term μBB · ∇π0 WZW-type term μBμIΩ · ∇π0 WZW-type term μ2BΩ · ∇η
In both cases under sufficiently fast rotation, the combination of the rotation-induced topological term for the η meson and the QCD anomaly leads to an inhomogeneous condensate of the η meson, known as the chiral soliton lattice (CSL)
We argue that these η CSL states at low density and high density should be continuously connected in flavor-symmetric QCD, extending the quark-hadron continuity conjecture [21,22,23] in the presence of the rotation
Summary
We consider the low-energy effective theory — the chiral perturbation theory (ChPT) — for low-density hadronic matter under rotation. (We will consider the effects of quark masses and the U(1)A anomaly later.) In this case, QCD has the U(3)R × U(3)L chiral symmetry: qR → e−iλ0θ0R VRqR , qL → e−iλ0θ0L VLqL ,. The indices A and a, b, c stand for A = 1, 2, · · · , 8 and a, b, c = 0, 1, · · · , 8, respectively We assume that this chiral symmetry is spontaneously broken down to the vector U(3)V symmetry in the vacuum and low-density hadronic matter. We can parametrize the field of the nonet mesons by the U(3) matrix U ,. Where gμν is an inverse matrix of the metric gμν in eq (1.1) This effective theory is based on the expansion in terms of the small parameter p/(4πfπ,η ) 1 with p being the momentum. We will take Ω/(4πfπ,η ) as a small expansion parameter and we will consider the leading-order contributions of Ω in the effective theory
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