Abstract:We provide a superselection theory of symmetry defects in 2+1D symmetry enriched topological (SET) order in the infinite volume setting. For a finite symmetry group $G$ with a unitary on-site action, our formalism produces a $G$-crossed braided tensor category $G\mathsf{Sec}$. This superselection theory is a direct generalization of the usual superselection theory of anyons, and thus is consistent with this standard analysis in the trivially graded component $G\mathsf{Sec}_1$. This framework also gives us a completely rigorous understanding of symmetry fractionalization. To demonstrate the utility of our formalism, we compute $G\mathsf{Sec}$ explicitly in both short-range and long-range entangled spin systems with symmetry and recover the relevant skeletal data.
From: Daniel Wallick [view email]
[v1]
Wed, 30 Oct 2024 18:34:49 UTC (270 KB)
[v2]
Mon, 24 Mar 2025 21:29:36 UTC (316 KB)
[v3]
Wed, 17 Jun 2026 15:43:42 UTC (321 KB)
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