源自 Godbillon-Vey 不变量的具有叶状结构与子维数粒子的新场论
New Field Theories with Foliation Structure and Subdimensional Particles from Godbillon-Vey Invariant
AI总结：
本文受 Godbillon-Vey 不变量启发构造类 BF 场论，以子系统高形式对称性及其自发破缺刻画 fracton 等子维数粒子的迁移率约束与次广延 GSD，并给出晶格实现及耦合动力学物质理论。
摘要：
近来，包括 fracton 在内的子维数粒子受到多个领域的广泛关注。这类物相的显著特征是迁移率约束以及次广延基态简并度（GSD）。本文中，我们受 Godbillon-Vey 不变量——叶状流形的一种数学不变量——启发，提出一种类 BF 理论。该理论包含子系统高形式对称性，这些对称性通过自发对称性破缺明确保证迁移率约束和次广延 GSD。我们还讨论了若干晶格自旋模型，它们实现了与该类 BF 理论相同的低能行为。此外，我们探究了与该类 BF 理论耦合的动力学物质理论。
英文摘要：
Recently, subdimensional particles including fractons have attracted much attention from various areas. Notable features of such matter phases are mobility constraints and subextensive ground state degeneracies (GSDs). In this paper, we propose a BF-like theory motivated by the Godbillon-Vey invariant, which is a mathematical invariant of the foliated manifold. Our theory hosts subsystem higher form symmetries which manifestly ensure the mobility constraint and subextensive GSD through the spontaneous symmetry breaking. We also discuss some lattice spin models which realize the same low energy behaviours as the BF-like theory. Furthermore, we explore dynamical matter theories which are coupled to the BF-like theory.
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