The Branes Behind Generalized Symmetry Operators

Understand

The modern approach to $m$-form global symmetries in a $d$-dimensional quantum field theory (QFT) entails specifying dimension $d-m-1$ topological generalized symmetry operators which non-trivially link with $m$-dimensional defect operators.

• In QFTs engineered via string constructions on a non-compact geometry $X$, these defects descend from branes wrapped on non-compact cycles which extend from a localized source / singularity to the boundary $\partial X$.
• The generalized symmetry operators which link with these defects arise from magnetic dual branes wrapped on cycles in $\partial X$.
• This provides a systematic way to read off various properties of such topological operators, including their worldvolume topological field theories, and the resulting fusion rules.