论文标题
无间隙系统中的拓扑质量产生
Topological mass generation in gapless systems
论文作者
论文摘要
可以通过间隙系统中的拓扑耦合（例如$（3+1）$ dimensions中的Abelian Higgs模型和Maxwell-Chern-Simons理论$（2+1）$尺寸，可以普遍描述量规场的质量生成。这些系统还表现出更高形式的$ \ mathbb {z} _k $ symmetries和级别$ k \ geq 2 $的拓扑订单的自发破坏。在本文中，我们考虑无间隙系统中的拓扑质量产生。作为一个范式的例子，我们研究了$ k $ in $ in $（3+1）$ dimensions的轴轴电动力学，在背景字段中均设有既有间隙和无间隙模式的尺寸。我们认为，间隙模式与较低维度的完全间隙系统中的模式有关。我们表明，尽管没有传统的拓扑顺序，但该系统表现出更高形式的$ \ mathbb {z} _k $对称性的自发破坏。在背景磁场的情况下，我们还通过二次分散关系得出了无间隙模式的低能量有效理论，并表明它满足了手性异常匹配。
Mass generation of gauge fields can be universally described by topological couplings in gapped systems, such as the Abelian Higgs model in $(3+1)$ dimensions and the Maxwell-Chern-Simons theory in $(2+1)$ dimensions. These systems also exhibit the spontaneous breaking of higher-form $\mathbb{Z}_k$ symmetries and topological orders for level $k \geq 2$. In this paper, we consider topological mass generation in gapless systems. As a paradigmatic example, we study the axion electrodynamics with level $k$ in $(3+1)$ dimensions in background fields that hosts both gapped and gapless modes. We argue that the gapped mode is related to those in fully gapped systems in lower dimensions via dimensional reduction. We show that this system exhibits the spontaneous breaking of a higher-form $\mathbb{Z}_k$ symmetry despite the absence of the conventional topological order. In the case of the background magnetic field, we also derive the low-energy effective theory of the gapless mode with the quadratic dispersion relation and show that it satisfies the chiral anomaly matching.
