$$C^*$$-Categorical Prefactorization Algebras for Superselection Sectors and Topological Order
Year: 2025
Type: article
Abstract: This paper presents a conceptual and efficient geometric framework to encode the algebraic structures on the category of superselection sectors of an algebraic quantum field theory on the n -dimensional lattice $$\mathbb {Z}^n$$ Z n . It is shown that, under the typical assumption of Haag duality, the monoidal $$C^*$$ C ∗ -categories of localized superselection sectors carry the structure of a locally constant prefactorization algebra over the category of cone-shaped subsets of $$\mathbb {Z}^n$$ Z n . Employing techniques from higher algebra, one extracts from this datum an underlying locally constant prefactorization algebra defined on open disks in the cylinder $$\mathbb {R}^1\times \mathbb {S}^{n-1}$$ R 1 × S n - 1 . While the sphere $$\mathbb {S}^{n-1}$$ S n - 1 arises geometrically as the angular coordinates of cones, the origin of the line $$\mathbb {R}^1$$ R 1 is analytic and rooted in Haag duality. The usual braided (for $$n=2$$ n = 2 ) or symmetric (for $$n\ge 3$$ n ≥ 3 ) monoidal $$C^*$$ C ∗ -categories of superselection sectors are recovered by removing a point of the sphere $$\mathbb {R}^1\times (\mathbb {S}^{n-1}\setminus \text {pt}) \cong \mathbb {R}^n$$ R 1 × ( S n - 1 \ pt ) ≅ R n and using the equivalence between $$\mathbb {E}_n$$ E n -algebras and locally constant prefactorization algebras defined on open disks in $$\mathbb {R}^n$$
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
OpenAlex ID: W4417114228