These are a set of lecture notes on generalized global symmetries in quantum field theory.
The focus is on invertible symmetries with a few comments regarding non-invertible …

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 …

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 …

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+ …

Symmetry-protected topological (SPT) phases are many-body quantum states that are
topologically nontrivial as long as the relevant symmetries are unbroken. In this work we …

A bstract A q-form global symmetry is a global symmetry for which the charged operators are
of space-time dimension q; eg Wilson lines, surface defects, etc., and the charged …

A bstract 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 …

We implement an extended version of reflection positivity (Wick-rotated unitarity) for
invertible topological quantum field theories and compute the abelian group of deformation …

A bstract It has been proposed recently that interacting Symmetry Protected Topological
Phases can be classified using cobordism theory. We test this proposal in the case of …

Solitonic symmetry has been believed to follow the homotopy-group classification of
topological solitons. Here, we point out a more sophisticated algebraic structure when …