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Gauging Categorical Symmetries in 3d Topological Orders and Bulk Reconstruction
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Gauging Categorical Symmetries in 3d Topological Orders and Bulk Reconstruction
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We use the language of categorical condensation to give a procedure for gauging nonabelian anyons, which are the manifestations of categorical symmetries in three spacetime dimensions. We also describe how the condensation procedure can be used in other contexts such as for topological cosets and constructing modular invariants. By studying a generalization of which anyons are condensable, we arrive at representations of congruence subgroups of the modular group. We finally present an analysis for ungauging anyons, which is related to the problem of constructing a Drinfeld center for a fusion category; this procedure we refer to as bulk reconstruction. We introduce a set of consistency relations regarding lines in the parent theory and wall category. Through use of these relations along with the $S$-matrix elements of the child theory, we construct $S$-matrix elements of a parent theory in a number of examples.
Forward citations
Cited by 9 Pith papers
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New dualities in 3d TQFTs are derived via non-invertible anyon condensation, generalizing level-rank dualities and providing new presentations for parafermion theories, c=1 orbifolds, and SU(2)_N.
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Sixteen-Fold Way for Fermionic Topological Orders
A sixteen-fold family of (2+1)D fermionic topological orders is identified, characterized by the mod-16 anomaly of a Z2 one-form symmetry and constructed as gapped boundaries of 3+1D fermionic SPT phases.
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Ensemble averaging in low-dimensional holography is reinterpreted as averaging over topological boundary conditions in a fixed SymTFT slab, reproducing Poisson moments in the Marolf-Maxfield model and Zamolodchikov me...
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Proliferation transitions from a topological phase in $2+1$ dimensions
A general 2+1d transition theory out of a topological phase, driven by one Abelian anyon, is constructed and shown to depend on a single integer parameter, with p=0 giving gauging.
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Higher Gauging and Non-invertible Condensation Defects
Higher gauging of 1-form symmetries on surfaces in 2+1d QFT yields condensation defects whose fusion rules involve 1+1d TQFTs and realizes every 0-form symmetry in TQFTs.
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Half dualization and non-invertible particle-vortex duality defect on lattice
Half dualization of the Villainized charge-n XY model produces a non-invertible particle-vortex duality defect whose fusion with its reverse yields a (1+1)D Z_n gauge theory.
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From Baby Universes to Narain Moduli: Topological Boundary Averaging in SymTFTs
Ensemble averaging in holography is reframed as averaging over topological completions of a relative theory via SymTFT boundary conditions, reproducing known moments in Marolf-Maxfield and Narain models.
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What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries
A survey of non-invertible symmetries with constructions in the Ising model and applications to neutral pion decay and other systems.
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Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond
This review summarizes transformative examples of generalized symmetries in QFT and their applications to anomalies and dynamics.
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