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Tannakian QFT: from spark algebras to quantum groups
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Tannakian QFT: from spark algebras to quantum groups
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We propose a nonperturbative construction of Hopf algebras that represent categories of line operators in topological quantum field theory, in terms of semi-extended operators (spark algebras) on pairs of transverse topological boundary conditions. The construction is a direct implementation of Tannakian formalism in QFT. Focusing on d=3 dimensional theories, we find topological definitions of R-matrices, ribbon twists, and the Drinfeld double construction for generalized quantum groups. We illustrate our construction in finite-group gauge theory, and apply it to obtain new results for B-twisted 3d $\mathcal{N}=4$ gauge theories, a.k.a. equivariant Rozansky-Witten theory, or supergroup BF theory (including ordinary BF theory with compact gauge group). We reformulate our construction mathematically in terms of abelian and dg tensor categories, and discuss connections with Koszul duality.
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Cited by 1 Pith paper
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Factorization Algebras and Quantum Groups from Generalized Poisson Sigma Models
Generalized Poisson sigma models realize deformation quantizations of holomorphic-topological factorization algebras and produce quantum groups as Koszul duals of their boundary algebras.
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