AI 中文总结
本文针对阿贝尔量子霍尔界面，采用空间重参数化不变的世界面描述，推导法向电荷输运与界面运动的关系，引入相对面积构造转化为等时约束，结合K矩阵电流代数确定通用霍尔运动学，为动力学量子霍尔界面有效理论提供系统基础。
AI 中文摘要
自由运动的量子霍尔界面与由外部约束势固定的普通边缘根本不同。由于法向位移会改变相邻不可压缩相占据的面积，界面几何与电荷动力学不能被视为独立自由度。我们针对阿贝尔量子霍尔相之间的界面，采用空间重参数化不变的世界面描述来构建该问题，其中切向运动是界面的重标记，而法向运动是物理的。从两侧的陈-西蒙斯响应出发，我们推导了法向电荷输运与界面运动之间的关系。随后我们引入了相对于材料参考曲线定义的相对面积构造，该构造将此速度关系转化为等时约束，该约束将带电边界扇区与界面形状关联起来。结合折叠的 K 矩阵电流代数，这确定了运动界面的通用霍尔运动学，同时其几何能量和中性动力学依赖于微观界面物理。所得框架为动力学量子霍尔界面的有效理论提供了系统基础。
英文摘要
A freely moving quantum Hall interface is fundamentally different from an ordinary edge fixed by an external confining potential. Since a normal displacement changes the areas occupied by the adjacent incompressible phases, the interface geometry and charge dynamics cannot be treated as independent degrees of freedom. We formulate this problem for interfaces between Abelian quantum Hall phases using a spatially reparametrization-invariant worldsheet description, in which tangential motion is a relabeling of the interface while normal motion is physical. Starting from the two-sided Chern--Simons response, we derive the relation between normal charge transport and interface motion. We then introduce a relative-area construction, defined with respect to a material reference curve, that converts this velocity relation into an equal-time constraint linking the charged boundary sector to the interface shape. Combined with the folded $K$-matrix current algebra, this identifies the universal Hall kinematics of the moving interface while leaving its geometric energy and neutral dynamics dependent on microscopic interface physics. The resulting framework provides a systematic basis for effective theories of dynamical quantum Hall interfaces.
Comments19 pages, 3 figures
