标题： QCD物质的相图与磁场：手征孤子晶格中的畴壁Skyrmion链 显示英文标题

标题： Phase diagram of QCD matter with magnetic field: domain-wall Skyrmion chain in chiral soliton lattice

摘要： 在强磁场中的QCD物质表现出丰富的相结构。 在外部磁场存在的情况下，两味的手征拉格朗日量伴随着Wess-Zumino-Witten（WZW）项，该项包含中性π介子$\pi_0$通过手征反常与磁场的异常耦合。 由于这一项，基态以非均匀形式存在，或者是手征孤子晶格（CSL），即沿着磁场方向排列的孤子阵列，或者是畴壁Skyrmion（DWSk）相，在这种相中，由$\pi_3[{\rm SU}(2)] \simeq {\mathbb Z}$支持的Skyrmion作为拓扑块出现在孤子内部，这些拓扑块由有效世界体积理论中的$\pi_2(S^2) \simeq {\mathbb Z}$支持。 在本文中，我们超越单孤子近似，在手征微扰理论的一阶下确定CSL和DWSk相之间的相边界。 为此，我们研究了在多个孤子配置中的畴壁Skyrmion链。 首先，我们通过模数近似构建CSL的有效理论，并得到${\mathbb C}P^1$模型或O(3)模型，该模型由背景电磁规范场规范，包含两种来自WZW项的拓扑项：一种是2+1维世界体积中的拓扑块电荷，另一种是计数孤子数的拓扑项。 在2+1维世界体积理论中的拓扑块是超导环，它们的大小受到通量量子化条件的约束。 块的负能条件给出了CSL和DWSk相之间的相边界。 我们发现，CSL内部的大区域被DWSk相占据，并且在相边界附近，CSL在DWSk相中仍保持亚稳态。 显示英文摘要

摘要： QCD matter in strong magnetic field exhibits a rich phase structure. In the presence of an external magnetic field, the chiral Lagrangian for two flavors is accompanied by the Wess-Zumino-Witten (WZW) term containing an anomalous coupling of the neutral pion $\pi_0$ to the magnetic field via the chiral anomaly. Due to this term, the ground state is inhomogeneous in the form of either chiral soliton lattice (CSL), an array of solitons in the direction of magnetic field, or domain-wall Skyrmion (DWSk) phase in which Skyrmions supported by $\pi_3[{\rm SU}(2)] \simeq {\mathbb Z}$ appear inside the solitons as topological lumps supported by $\pi_2(S^2) \simeq {\mathbb Z}$ in the effective worldvolume theory of the soliton. In this paper, we determine the phase boundary between the CSL and DWSk phases beyond the single-soliton approximation, within the leading order of chiral perturbation theory. To this end, we explore a domain-wall Skyrmion chain in multiple soliton configurations. First, we construct the effective theory of the CSL by the moduli approximation, and obtain the ${\mathbb C}P^1$ model or O(3) model, gauged by a background electromagnetic gauge field, with two kinds of topological terms coming from the WZW term: one is the topological lump charge in 2+1 dimensional worldvolume and the other is a topological term counting the soliton number. Topological lumps in the 2+1 dimensional worldvolume theory are superconducting rings and their sizes are constrained by the flux quantization condition. The negative energy condition of the lumps yields the phase boundary between the CSL and DWSk phases. We find that a large region inside the CSL is occupied by the DWSk phase, and that the CSL remains metastable in the DWSk phase in the vicinity of the phase boundary.