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

Generalized symmetries (also known as categorical symmetries) is a newly developing
technique for studying quantum field theories. It has given us new insights into the structure …

In this paper we use the AdS/CFT correspondence to refine and then establish a set of old
conjectures about symmetries in quantum gravity. We first show that any global symmetry …

For a zero-temperature Landau symmetry-breaking transition in n-dimensional space that
completely breaks a finite symmetry G, the critical point at the transition has the symmetry G …

We review developments in the theory of multiple, parallel membranes in M-theory. After
discussing the inherent difficulties with constructing a maximally supersymmetric lagrangian …

Symmetry is usually defined via transformations described by a (higher) group. But a
symmetry really corresponds to an algebra of local symmetric operators, which directly …

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 …

We present simple lattice realizations of symmetry-protected topological phases with q-form
global symmetries where charged excitations have q spatial dimensions. Specifically, we …

It was recently argued that quantum field theories possess one‐form and higher‐form
symmetries, labelled 'generalized global symmetries.'In this paper, we describe how those …

Trivially-acting symmetries in two-dimensional conformal field theory include twist fields of
dimension zero which are local topological operators. We investigate the consequences of …