What comprises a global symmetry of a Quantum Field Theory (QFT) has been vastly
expanded in the past 10 years to include not only symmetries acting on higher-dimensional …

There are two prominent applications of the mathematical concept of topology to the physics
of materials: band topology, which classifies different topological insulators and semimetals …

We identify infinitely many noninvertible generalized global symmetries in QED and QCD for
the real world in the massless limit. In QED, while there is no conserved Noether current for …

We elucidate the fate of classical symmetries which suffer from Abelian Adler-Bell-Jackiw
anomalies. Instead of being completely destroyed, these symmetries survive as …

The theory of entanglement provides a fundamentally new language for describing
interactions and correlations in many-body systems. Its vocabulary consists of qubits and …

We discuss invertible and non-invertible topological condensation defects arising from
gauging a discrete higher-form symmetry on a higher codimensional manifold in spacetime …

Given any symmetry acting on ad-dimensional quantum field theory, there is an associated
(d+ 1)-dimensional topological field theory known as the Symmetry TFT (SymTFT). The …

We discuss a variety of codimension-one, non-invertible topological defects in general 3+ 1d
QFTs with a discrete one-form global symmetry. These include condensation defects from …

We sketch a procedure to capture general non-invertible symmetries of a $ d $-dimensional
quantum field theory in the data of a higher-category, which captures the local properties of …

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 …