We study p-string condensation mechanisms for fracton phases from the viewpoint of higher-form symmetry, focusing on the examples of the X-cube model and the rank-two symmetric-tensor U(1) scalar charge theory. This work is motivated by questions of the relationship between fracton phases and continuum quantum field theories, and also provides general principles to describe p-string condensation independent of specific lattice model constructions. We give a perspective on higher-form symmetry in lattice models in terms of cellular homology. Applying this perspective to the coupled-layer construction of the X-cube model, we identify a foliated 1-form symmetry that is broken in the X-cube phase, but preserved in the phase of decoupled toric code layers. Similar considerations for the scalar charge theory lead to a framed 1-form symmetry. These symmetries are distinct from standard 1-form symmetries that arise, for instance, in relativistic quantum field theory. We also give a general discussion on interpreting p-string condensation, and related constructions involving gauging of symmetry, in terms of higher-form symmetry.

中文翻译：

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通过奇异的高形式对称破缺的分形相

我们从更高形式对称性的角度研究了分形相的 p 弦凝聚机制，重点是 X 立方模型和二阶对称张量 U(1) 标量电荷理论的例子。这项工作的动机是分形相和连续量子场论之间的关系问题，并且还提供了描述独立于特定晶格模型构造的 p 弦凝聚的一般原则。我们从细胞同源性的角度给出了晶格模型中更高形式对称性的观点。将此观点应用于 X 立方体模型的耦​​合层构造，我们确定了叶状 1 型对称性，该对称性在 X 立方体阶段被破坏，但在解耦复曲面代码层阶段得以保留。对标量电荷理论的类似考虑导致了框架 1 型对称。这些对称性不同于标准的 1 型对称性，例如在相对论量子场论中出现的对称性。我们还对解释 p 弦凝聚以及涉及测量对称性的相关构造进行了一般性讨论，根据更高形式的对称性。