偶极对称性的Chern-Simons理论
A Chern-Simons theory for dipole symmetry
AI总结：
本文提出一种包含U(1)和偶极规范场的Chern-Simons有效场论框架，用于描述偶极对称拓扑物质，并揭示了其维度普适性、边界依赖的体-边对应及与分形子-弹性对偶的联系。
摘要：
我们提出了可由Chern-Simons理论描述的偶极对称拓扑物质的有效场论。与大多数使用高阶规范理论的研究不同，我们发展了一个同时包含U(1)和偶极规范场的框架。因此，只有最高多重极对称性才能支持't Hooft反常。我们表明，在适当的点群对称性下，偶极Chern-Simons理论可以存在于任何维度，而且体-边对应可以依赖于边界。作为两个应用，我们将偶极反常与扭转反常进行了类比，并将粒子-涡旋对偶推广到偶极相变。以上所有内容都在平直时空极限内，但我们的框架能够系统地将偶极对称性与弯曲时空耦合。基于此，我们提出了关于反常偶极流体动力学的建议。此外，我们证明了分形子-弹性对偶自然地产生于三维非阿贝尔Chern-Simons理论。
英文摘要：
We present effective field theories for dipole symmetric topological matters that can be described by the Chern-Simons theory. Unlike most studies using higher-rank gauge theory, we develop a framework with both U(1) and dipole gauge fields. As a result, only the highest multipole symmetry can support the 't Hooft anomaly. We show that with appropriate point group symmetries, the dipolar Chern-Simons theory can exist in any dimension and, moreover, the bulk-edge correspondence can depend on the boundary. As two applications, we draw an analogy between the dipole anomaly and the torsional anomaly and generalize particle-vortex duality to dipole phase transitions. All of the above are in the flat spacetime limit, but our framework is able to systematically couple dipole symmetry to curved spacetime. Based on that, we give a proposal about anomalous dipole hydrodynamics. Moreover, we show that the fracton-elasticity duality arises naturally from a non-abelian Chern-Simons theory in 3D.
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