论文标题
2+1D紧凑型Lifshitz理论，张量规理论和分布量
2+1d Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons
论文作者
论文摘要
自由紧凑型标量场的2+1D连续体Lifshitz理论在凝结物理学和高能量物理学中在多种量子系统中起着重要作用。众所周知，在紧凑的空间中，它具有无限的基态变性。为了更好地理解这一理论，我们考虑使用修改后的反派形式主义对其进行两个候选晶格正规化。我们表明，这两种晶格理论具有明显不同的全球对称性（包括偶极性全球对称性），异常，基础状态变性和二元性。特别是，其中一个是自偶联。鉴于这些理论及其全球对称性，我们可以将它们与相应的仪表理论相提并论。这是两个不同的$ u（1）$张量表理论。产生的模型具有限制的迁移率的激发功能，即分布量。最后，我们为LIFSHITZ理论，标量和矢量电荷量规理论提供了晶格/lineon弹性双重性的确切晶格实现。
The 2+1d continuum Lifshitz theory of a free compact scalar field plays a prominent role in a variety of quantum systems in condensed matter physics and high energy physics. It is known that in compact space, it has an infinite ground state degeneracy. In order to understand this theory better, we consider two candidate lattice regularizations of it using the modified Villain formalism. We show that these two lattice theories have significantly different global symmetries (including a dipole global symmetry), anomalies, ground state degeneracies, and dualities. In particular, one of them is self-dual. Given these theories and their global symmetries, we can couple them to corresponding gauge theories. These are two different $U(1)$ tensor gauge theories. The resulting models have excitations with restricted mobility, i.e., fractons. Finally, we give an exact lattice realization of the fracton/lineon-elasticity dualities for the Lifshitz theory, scalar and vector charge gauge theories.
