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 …

The most well-known mechanism for fermions to acquire a mass is the Nambu–Goldstone–
Anderson–Higgs mechanism, ie, after a spontaneous symmetry breaking, a bosonic field …

A bstract We revisit the symmetries of massless two-dimensional adjoint QCD with gauge
group SU (N). The dynamics is not sufficiently constrained by the ordinary symmetries and …

A fundamental distinction between many-body quantum states are those with short-and long-
range entanglement (SRE and LRE). The latter cannot be created by finite-depth circuits …

We survey recent developments in a novel kind of generalized global symmetry, the non-
invertible symmetry, in diverse spacetime dimensions. We start with several different but …

Generalized symmetries often appear in the form of emergent symmetries in low energy
effective descriptions of quantum many-body systems. Non-invertible symmetries are a …

A global symmetry (0-symmetry) in an n-dimensional space acts on the whole space. A
higher symmetry acts on closed submanifolds (ie, loops and membranes, etc.), and those …

We investigate mixed states exhibiting nontrivial topological features, focusing on symmetry-
protected topological (SPT) phases under various types of decoherence. Our findings …

Anomalies of global symmetries are important tools for understanding the dynamics of
quantum systems. We investigate anomalies of non-invertible symmetries in 3+ 1d using 4+ …

A bstract 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) …