Symmetry breaking

Quantum mechanics

Theoretical physics

Spacetime symmetries

Quantum field theory in curved spacetime

Spacetime

Mathematical physics

Quantum gravity

Symmetry group

Global symmetry

Physics

Mathematics

Homogeneous space

Spontaneous symmetry breaking

Geometry

Quantum

Symmetry (geometry)

Group (periodic table)

Journal of High Energy Physics

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 phenomenon in detail using the language of symmetry defects. We exhibit a simple procedure to determine the (possible) 2-group global symmetry of a given QFT, and provide a classification of the related 't Hooft anomalies (for symmetries not acting on spacetime). We also describe how QFTs can be coupled to extrinsic backgrounds for symmetry groups that differ from the intrinsic symmetry acting faithfully on the theory. Finally, we provide a variety of examples, ranging from TQFTs (gapped systems) to gapless QFTs. Along the way, we stress that the "obstruction to symmetry fractionalization" discussed in some condensed matter literature is really an instance of 2-group global symmetry.

On 2-group global symmetries and their anomalies