Explicit lattice constructions of gauging interfaces and condensation defects are given for higher-dimensional systems with higher-form symmetries, using movement operators to manage constrained Hilbert spaces.
Noninvertible duality de- fects in 3+1 dimensions
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Topological quantum critical points between chiral topological orders are captured by a non-compact conformal manifold whose topological angle satisfies Θ_cft^{-1} = ½(Θ₁^{-1} + Θ₂^{-1}).
Decohered non-Abelian Kitaev quantum double states exhibit strong-to-weak spontaneous symmetry breaking of non-invertible higher-form symmetries and form an information convex set whose dimension equals the pure-state ground-state degeneracy.