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- W4378347232 abstract "We discuss invertible and non-invertible topological condensation defects arising from gauging a discrete higher-form symmetry on a higher codimensional manifold in spacetime, which we define as higher gauging. A $q$-form symmetry is called $p$-gaugeable if it can be gauged on a codimension-$p$ manifold in spacetime. We focus on 1-gaugeable 1-form symmetries in general 2+1d QFT, and gauge them on a surface in spacetime. The universal fusion rules of the resulting invertible and non-invertible condensation surfaces are determined. In the special case of 2+1d TQFT, every (invertible and non-invertible) 0-form global symmetry, including the $mathbb{Z}_2$ electromagnetic symmetry of the $mathbb{Z}_2$ gauge theory, is realized from higher gauging. We further compute the fusion rules between the surfaces, the bulk lines, and lines that only live on the surfaces, determining some of the most basic data for the underlying fusion 2-category. We emphasize that the fusion coefficients in these non-invertible fusion rules are generally not numbers, but rather 1+1d TQFTs. Finally, we discuss examples of non-invertible symmetries in non-topological 2+1d QFTs such as the free $U(1)$ Maxwell theory and QED." @default.
- W4378347232 created "2023-05-27" @default.
- W4378347232 creator A5001999970 @default.
- W4378347232 creator A5057549587 @default.
- W4378347232 creator A5085880592 @default.
- W4378347232 date "2023-05-08" @default.
- W4378347232 modified "2023-10-18" @default.
- W4378347232 title "Higher Gauging and Non-invertible Condensation Defects" @default.
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- W4378347232 doi "https://doi.org/10.1007/s00220-023-04706-9" @default.
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