Dense quantum chromodynamic matter accommodates various kind of topological solitons such as vortices, domain walls, monopoles, kinks, boojums, and so on. In this review, we discuss various properties of topological solitons in dense quantum chromodynamics (QCD) and their phenomenological implications. Particular emphasis is placed on the topological solitons in the color–flavor-locked (CFL) phase, which exhibits both superfluidity and superconductivity. The properties of topological solitons are discussed in terms of effective field theories such as the Ginzburg–Landau theory, the chiral Lagrangian, or the Bogoliubov–de Gennes equation. The most fundamental string-like topological excitations in the CFL phase are non-Abelian vortices, which are 1/3 quantized superfluid vortices and color magnetic flux tubes. These vortices are created at a phase transition by the Kibble–Zurek mechanism or when the CFL phase is realized in compact stars, which rotate rapidly. The interaction between vortices is found to be repulsive and consequently a vortex lattice is formed in rotating CFL matter. Bosonic and fermionic zero-energy modes are trapped in the core of a non-Abelian vortex and propagate along it as gapless excitations. The former consists of translational zero modes (a Kelvin mode) with a quadratic dispersion and ${mathbb {C}}P^2$ Nambu–Goldstone gapless modes with a linear dispersion, associated with the CFL symmetry spontaneously broken in the core of a vortex, while the latter is Majorana fermion zero modes belonging to the triplet of the symmetry remaining in the core of a vortex. The low-energy effective theory of the bosonic zero modes is constructed as a non-relativistic free complex scalar field and a relativistic ${mathbb {C}}P^2$ model in 1+1 dimensions. The effects of strange quark mass, electromagnetic interactions, and non-perturbative quantum corrections are taken into account in the ${mathbb {C}}P^2$ effective theory. Various topological objects associated with non-Abelian vortices are studied; colorful boojums at the CFL interface, the quantum color magnetic monopole confined by vortices, which supports the notion of quark–hadron duality, and Yang–Mills instantons inside a non-Abelian vortex as lumps are discussed. The interactions between a non-Abelian vortex and quasiparticles such as phonons, gluons, mesons, and photons are studied. As a consequence of the interaction with photons, a vortex lattice behaves as a cosmic polarizer. As a remarkable consequence of Majorana fermion zero modes, non-Abelian vortices are shown to behave as a novel kind of non-Abelian anyon. In the order parameters of chiral symmetry breaking, we discuss fractional and integer axial domain walls, Abelian and non-Abelian axial vortices, axial wall–vortex composites, and Skyrmions.
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机译：密集的量子色动力物质可容纳各种拓扑孤子，例如涡旋，畴壁，单极子，扭结，浮筒等。在这篇综述中，我们讨论了稠密量子色动力学（QCD）中拓扑孤子的各种特性及其现象学意义。特别强调的是色香味锁定（CFL）相中的拓扑孤子，该孤子既表现出超流动性，又表现出超导电性。拓扑孤子的性质根据有效的场论进行了讨论，例如Ginzburg–Landau理论，手性拉格朗日方程或Bogoliubov–de Gennes方程。 CFL相中最基本的弦状拓扑激发是非阿贝尔涡旋，它们是1/3量化的超流体涡旋和彩色磁通管。这些涡旋是在通过Kibble-Zurek机理发生相变时产生的，或者是当CFL相位在快速旋转的紧凑恒星中实现时产生的。发现涡旋之间的相互作用是排斥的，因此在旋转的CFL物质中形成了涡旋晶格。玻色子和费米子零能模式被捕获在非阿贝尔涡旋的核心中，并作为无间隙激发沿其传播。前者由具有二次弥散的平移零模（开尔文模）和具有线性弥散的$ {mathbb {C}} P ^ 2 $ Nambu–Goldstone无隙模组成，与CFL对称性自发破裂旋涡，而后者是马约拉那费米子零模，属于旋涡核心的对称三重态。玻色子零模的低能效理论被构造为一个非相对论的自由复标量场和一个相对论的$ {mathbb {C}} P ^ 2 $模型，其维数为1 + 1。 $ {mathbb {C}} P ^ 2 $有效理论考虑了奇怪的夸克质量，电磁相互作用和非扰动量子校正的影响。研究了与非阿贝尔涡旋有关的各种拓扑对象。 CFL界面上的彩色boojums，受涡旋限制的量子色磁性单极子（支持夸克-强子对偶性的概念）以及非阿贝尔涡旋内的Yang-Mills瞬子作为团块进行了讨论。研究了非阿贝尔涡旋与准粒子（如声子，胶子，介子和光子）之间的相互作用。作为与光子相互作用的结果，涡旋晶格表现为宇宙偏振器。作为马里亚纳费米子零模的显着结果，非阿贝尔涡旋表现为一种新型的非阿贝尔涡旋。在手性对称破坏的顺序参数中，我们讨论了分数和整数轴向畴壁，Abelian和非Abelian轴向涡旋，轴向壁-涡旋复合体和Skyrmions。
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