论文标题
全球偶极对称性，紧凑型Lifshitz理论，张量规理论和分形量
Global Dipole Symmetry, Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons
论文作者
论文摘要
我们研究了具有全局偶极对称性和级偶极子对称性的田间理论。著名的Lifshitz理论是具有全球偶极对称性理论的一个例子。我们详细研究了其1+1D版本的紧凑字段。当将此全局对称性促进到$ u（1）$偶极仪表对称性时，相应的量规场是一个张量规场。众所周知，该理论会导致分形剂。为了以这些全局或规格对称性的精确含义解决各种微妙之处，我们将这1+1D理论放在晶格上，然后采取连续限制。有趣的是，连续限制不是唯一的。不同的限制导致不同的连续理论，其操作员，缺陷，全局对称性等不同。我们还考虑使用$ \ mathbb z_n $ Dipole Gauge组的晶格仪理论。令人惊讶的是，几种物理可观察的物质，例如基态退化和缺陷的迁移率，取决于晶格中的地点数量。 我们的分析迫使我们仔细考虑不对理论的标准希尔伯特空间作用的全球对称性，而只能在缺陷的存在下对希尔伯特的空间。我们将它们称为类似时间的全球对称性，并详细讨论它们。这些时间式的全局对称性使我们能够用全球对称性的结果表达缺陷的移动性限制（包括分形式）。
We study field theories with global dipole symmetries and gauge dipole symmetries. The famous Lifshitz theory is an example of a theory with a global dipole symmetry. We study in detail its 1+1d version with a compact field. When this global symmetry is promoted to a $U(1)$ dipole gauge symmetry, the corresponding gauge field is a tensor gauge field. This theory is known to lead to fractons. In order to resolve various subtleties in the precise meaning of these global or gauge symmetries, we place these 1+1d theories on a lattice and then take the continuum limit. Interestingly, the continuum limit is not unique. Different limits lead to different continuum theories, whose operators, defects, global symmetries, etc. are different. We also consider a lattice gauge theory with a $\mathbb Z_N$ dipole gauge group. Surprisingly, several physical observables, such as the ground state degeneracy and the mobility of defects depend sensitively on the number of sites in the lattice. Our analysis forces us to think carefully about global symmetries that do not act on the standard Hilbert space of the theory, but only on the Hilbert space in the presence of defects. We refer to them as time-like global symmetries and discuss them in detail. These time-like global symmetries allow us to phrase the mobility restrictions of defects (including those of fractons) as a consequence of a global symmetry.
