凝聚态物质中的广义对称性

Generalized Global Symmetries

A $q$-form global symmetry is a global symmetry for which the charged operators are of space-time dimension $q$; e.g. Wilson lines, surface defects, etc., and the charged excitations have $q$ spatial dimensions; e.g. strings, membranes, etc. Many of the properties of ordinary global symmetries ($q$=0) apply here. They lead to Ward identities and hence to selection rules on amplitudes. Such global symmetries can be coupled to classical background fields and they can be gauged by summing over these classical fields. These generalized global symmetries can be spontaneously broken (either complete…

On 2-Group Global Symmetries and Their Anomalies

In general quantum field theories (QFTs), ordinary (0-form) global symmetries and 1-form symmetries can combine into 2-group global symmetries. We describe this phenomenon in detail using the language of symmetry defects. We exhibit a simple procedure to determine the (possible) 2-group global symmetry of a given QFT, and provide a classification of the related 't Hooft anomalies (for symmetries not acting on spacetime). We also describe how QFTs can be coupled to extrinsic backgrounds for symmetry groups that differ from the intrinsic symmetry acting faithfully on the theory. Finally, we prov…

Generalized Symmetries of the Graviton

We find the set of generalized symmetries associated with the free graviton theory in four dimensions. These are generated by gauge invariant topological operators that violate Haag duality in ring-like regions. As expected from general QFT grounds, we find a set of "electric" and a dual set of "magnetic'" topological operators and compute their algebra. To do so, we describe the theory using phase space gauge-invariant electric and magnetic dual variables constructed out of the curvature tensor. Electric and magnetic fields satisfy a set of constraints equivalent to the ones of a stress tenso…

广义调制对称性与 $\mathbb{Z}_2$ 拓扑有序相

Generalized Modulated Symmetries in $\mathbb{Z}_2$ Topological Ordered Phases

研究2+1维$\mathbb{Z}_2$拓扑有序相中的广义调制对称性，发现其导致基态对晶格尺寸依赖、任意子刚性步长移动及丰富边界相，并通过有效场论统一描述。

混合态中广义对称性保护拓扑相的推广

Generalized symmetry-protected topological phases in mixed states from gauging dualities

本文研究混合态中广义对称性保护拓扑相的分类，通过 gauge 对应将广义对称性与普通群对称性联系起来，利用字符串序参数和保护边缘模式描述非可逆和偶极对称性的ASPT相。

Effective field theory of magnetohydrodynamics from generalized global symmetries

We introduce an effective action for non-dissipative magnetohydrodynamics. A crucial guiding principle is the generalized global symmetry of electrodynamics, which naturally leads to introducing a "dual photon" as the degree of freedom responsible for the electromagnetic component of the fluid. The formalism includes additional degrees of freedom and symmetries which characterize the hydrodynamic regime. By suitably enhancing one of the symmetries, the theory becomes force-free electrodynamics. The symmetries furthermore allow to systematize local and non-local conserved helicities. We also di…

Note on Generalized Symmetries, Gapless Excitations, Generalized Symmetry Protected Topological states, and Anomaly

We consider quantum many body systems with generalized symmetries, such as the higher form symmetries introduced recently, and the "tensor symmetry". We consider a general form of lattice Hamiltonians which allow a certain level of nonlocality. Based on the assumption of dual generalized symmetries, we explicitly construct low energy excited states. We also derive the 't Hooft anomaly for the general Hamiltonians after "gauging" the dual generalized symmetries. A 3d system with dual anomalous 1-form symmetries can be viewed as the boundary of a 4d generalized symmetry protected topological (SP…

On symmetries of generalized Calogero model and Polychronakos-Frahm chain

The symmetry of the generalized Polychronakos-Frahm chain is obtained from the Dunkl-operator deformation of the unitary algebra, which describes the symmetry of the generalized Calogero model.

Jena广义全局对称性讲义：原理与应用

Jena lectures on generalized global symmetries: principles and applications

该讲义面向具量子场论基础的读者，介绍高形式等广义全局对称性的原理，并探讨其在规范理论、统计力学、反常及磁流体力学等知名模型中的应用。

局部交换投影模型中的广义霍尔电导率：广义对称性与保护的表面模式

Generalized Hall Conductivities in Local Commuting Projector Models: Generalized Symmetries and Protected Surface Modes

本文提出在局部交换投影模型中实现非零广义霍尔电导率的方法，通过修改的Villain形式法构建保护无能隙边界，并利用表面电流和多体陈数计算广义霍尔电导率。

QFTs的广义族

Generalized Families of QFTs

将族反常推广到破缺的广义/范畴对称性（包括高群和不可逆对称性），利用SymTFT研究RG流和红外相约束，并应用于4d类QCD理论。

ICTP关于（非）可逆广义对称性的讲座

ICTP Lectures on (Non-)Invertible Generalized Symmetries

本讲座系统介绍QFT中的广义对称性，重点通过TQFT stacking与规范构造非可逆theta缺陷，并讨论higher-representation及SymTFT。

Physics of Symmetry Protected Topological phases involving Higher Symmetries and their Applications

We discuss physical constructions, and the boundary properties of various symmetry protected topological phases that involve 1-form symmetries, from one spatial dimension (1d) to four spatial dimensions (4d). For example, the prototype 3d boundary state of 4d SPT states involving 1-form symmetries can be either a gapless photon phase (quantum electrodynamics) or gapped topological order enriched by 1-form symmetries, namely the loop excitations of these topological orders carry nontrivial 1-form symmetry charges. This study also serves the purpose of diagnosing anomaly of 3d states of matter. …

广义对称性与对称积 orbifold 的变形

Generalized Symmetries and Deformations of Symmetric Product Orbifolds

本文研究了对称积 orbifold CFTs 中的广义对称性，揭示了在特定条件下只有invertible和最大对称性能被保持，并探讨了其对 holography 的影响。

对非可逆对称性的规范化：拓扑界面与广义 orbifold 群oids 在 2d 量子场论中

Gauging Non-Invertible Symmetries: Topological Interfaces and Generalized Orbifold Groupoid in 2d QFT

本文研究了二维量子场论中非可逆对称性的规范化，通过拓扑界面和广义 orbifold 群oids 探讨其结构和性质，揭示了规范化的数学框架和物理意义。

从广义Lieb-Schultz-Mattis异常中获得调制对称性

Modulated symmetries from generalized Lieb-Schultz-Mattis anomalies

研究通过广义Lieb-Schultz-Mattis异常中的规范化对称性，揭示了调制对称性和偶极子代数的出现，并构建了二维、三维以及任意维度的晶格模型，连接了LSM异常流入与更高群对称结构。

Generalized Global Symmetries of $T[M]$ Theories. I

We study reductions of 6d theories on a $d$-dimensional manifold $M_d$, focusing on the interplay between symmetries, anomalies, and dynamics of the resulting $(6-d)$-dimensional theory $T[M_d]$. We refine and generalize the notion of "polarization" to "polarization on $M_d$," which serves to fix the spectrum of local and extended operators in $T[M_d]$. Another important feature of theories $T[M_d]$ is that they often possess higher-group symmetries, such as 2-group and 3-group symmetries. We study the origin of such symmetries as well as physical implications including symmetry breaking and s…

Descriptors for Machine Learning Model of Generalized Force Field in Condensed Matter Systems

We outline the general framework of machine learning (ML) methods for multi-scale dynamical modeling of condensed matter systems, and in particular of strongly correlated electron models. Complex spatial temporal behaviors in these systems often arise from the interplay between quasi-particles and the emergent dynamical classical degrees of freedom, such as local lattice distortions, spins, and order-parameters. Central to the proposed framework is the ML energy model that, by successfully emulating the time-consuming electronic structure calculation, can accurately predict a local energy base…

Topological features of ground states and topological solitons in generalized Su-Schrieffer-Heeger models using generalized time-reversal, particle-hole, and chiral symmetries

Topological phases and their topological features are enriched by the fundamental time-reversal, particle-hole, and chiral as well as crystalline symmetries. While one-dimensional (1D) generalized Su-Schrieffer-Heeger (SSH) systems show various topological phenomena such as topological solitons and topological charge pumping, it remains unclear how such symmetry protects and relates such topological phenomena. Here we show that the generalized time-reversal, particle-hole, and chiral symmetry operators consistently explain not only the symmetry transformation properties between the ground stat…