Higher Gauging and Non-invertible Condensation Defects

By Konstantinos Roumpedakis, Sahand Seifnashri, Shu-Heng Shao. Communications in Mathematical Physics, 2022

246 citations recorded by the source corpus.

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 $${\mathbb {Z}}_2$$ Z 2 electromagnetic symmetry of the $${\mathbb {Z}}_2$$ 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e0bbf30e15dda91893ca495afe7d1038234775aa

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Citations in the corpus

Universal Non‐Invertible Symmetries (2022, methodology): “In section 4 we study the relation of the above dual symmetries C 2 for S = Γ (0) being a finite 0-form symmetry to the condensation defects constructed using higher gauging of other symmetries [6, 7].”