In this lecture note, we give a basic introduction to the rapidly develo** concepts of
generalized symmetries, from the perspectives of both high energy physics and condensed …

Compass models are theories of matter in which the couplings between the internal spin (or
other relevant field) components are inherently spatially (typically, direction) dependent. A …

Symmetry plays a central role in quantum field theory. Recent developments include
symmetries that act on defects and other subsystems, and symmetries that are categorical …

We introduce a generalization of conventional lattice gauge theory to describe fracton
topological phases, which are characterized by immobile, pointlike topological excitations …

We explore non-invertible symmetries in two-dimensional lattice models with subsystem
$\mathbb Z_2 $ symmetry. We introduce a subsystem $\mathbb Z_2 $-gauging procedure …

In this work, we introduce a new type of topological order that is protected by subsystem
symmetries that act on lower-dimensional subsets of lattice many-body system, eg, along …

We continue our exploration of exotic, gapless lattice and continuum field theories with
subsystem global symmetries. In an earlier paper, we presented free lattice models enjoying …

A bstract We investigate a higher-group structure of massless axion electrodynamics in (3+
1) dimensions. By using the background gauging method, we show that the higher-form …

One of the most spectacular phenomena in physics in terms of dynamical range is the glass
transition and the associated slowing down of flow and relaxation with decreasing …

Multipole symmetries are of interest both as a window on fracton physics and as a crucial
ingredient in realizing new universality classes for quantum dynamics. Here we address the …