Higher Gauging and Non-invertible Condensation Defects

We discuss invertible and non-invertible topological condensation defects arising from gauging a discrete higher-form symmetry on higher codimensional manifold in spacetime, which we define as gauging. A $q$-form is called $p$-gaugeable if it can be gauged codimension-$p$ spacetime. focus 1-gaugeable 1-form symmetries general 2+1d QFT, gauge them surface The universal fusion rules of the resulting surfaces are determined. In special case TQFT, every (invertible non-invertible) 0-form global symmetry, including $\mathbb{Z}_2$ electromagnetic theory, realized further compute between surfaces, bulk lines, lines that only live determining some most basic data for underlying 2-category. emphasize "coefficients" these generally not numbers, but rather 1+1d TQFTs. Finally, examples non-topological QFTs such free $U(1)$ Maxwell theory QED.