世界面修补、1-形式对称性与“朗道星”相变
Worldsheet patching, 1-form symmetries, and "Landau-star" phase transitions
AI总结：
本研究针对2+1维$\boldsymbol{\text{Z}}_2$规范理论中膜孔洞破坏微观高形式对称性与弦可观测量的问题，提出膜修补方法恢复对称性，验证其数值实用性并分析准局域性与自对偶多临界点行为。
摘要：
规范理论相变的分析在很大程度上依赖于相图边界处出现的简化条件，在这些边界上某些激发是被禁止的。以2+1维$\boldsymbol{\text{Z}}_2$规范理论为例，这种简化可以通过几何方式可视化：在相图边界上，配分函数是闭膜的系综。然而更普遍的情况是，膜上存在“孔洞”，它们代表虚拟任意子激发的世界线。如果孔洞尺寸有限，通常它们不会影响普适类，但会破坏微观（高形式）对称性和微观（弦）可观测量。我们展示了如何通过“膜修补”程序恢复这些对称性和可观测量，该程序将膜系综映射回闭膜系综（这与“最小规范”中的规范固定思想密切相关，但并不等价）。膜修补使高对称性的涌现变得具体可感。我们在蒙特卡洛模拟中采用合适的算法执行修补操作，证明该方法能提供具有数值实用性的可观测量。例如，可以利用在临界点处呈幂律行为的关联函数来分析禁闭相变。我们分析了修补程序的准局域性，并讨论了规范-希格斯模型中自对偶多临界点处的情况——在该临界点处，表征孔洞的长度标度$\boldsymbol{\text{ℓ}}$会发散。
英文摘要：
The analysis of phase transitions of gauge theories has relied heavily on simplifications that arise at the boundaries of phase diagrams, where certain excitations are forbidden. Taking 2+1 dimensional $\mathbb{Z}_2$ gauge theory as an example, the simplification can be visualized geometrically: on the phase diagram boundaries the partition function is an ensemble of closed membranes. More generally, however, the membranes have "holes" in them, representing worldlines of virtual anyon excitations. If the holes are of a finite size, then typically they do not affect the universality class, but they destroy microscopic (higher-form) symmetries and microscopic (string) observables. We demonstrate how these symmetries and observables can be restored using a "membrane patching" procedure, which maps the ensemble of membranes back to an ensemble of closed membranes. (This is closely related to the idea of gauge fixing in the "minimal gauge", though not equivalent.) Membrane patching makes the emergence of higher symmetry concrete. Performing patching in a Monte Carlo simulation with an appropriate algorithm, we show that it gives access to numerically useful observables. For example, the confinement transition can be analyzed using a correlation function that is a power law at the critical point. We analyze the quasi-locality of the patching procedure and discuss what happens at a self-dual multicritical point in the gauge-Higgs model, where the lengthscale $\ell$ characterizing the holes diverges.
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