Constructs BF-like 3D SymTFT Lagrangians for finite non-Abelian groups presented as extensions, yielding surface-attaching non-genuine line operators and Drinfeld-center fusion rules.
Dualizable tensor categories
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abstract
We investigate the relationship between the algebra of tensor categories and the topology of framed 3-manifolds. On the one hand, tensor categories with certain algebraic properties determine topological invariants. We prove that fusion categories of nonzero global dimension are 3-dualizable, and therefore provide 3-dimensional 3-framed local field theories. We also show that all finite tensor categories are 2-dualizable, and yield categorified 2-dimensional 3-framed local field theories. On the other hand, topological properties of 3-framed manifolds determine algebraic equations among functors of tensor categories. We show that the 1-dimensional loop bordism, which exhibits a single full rotation, acts as the double dual autofunctor of a tensor category. We prove that the 2-dimensional belt-trick bordism, which unravels a double rotation, operates on any finite tensor category, and therefore supplies a trivialization of the quadruple dual. This approach produces a quadruple-dual theorem for suitably dualizable objects in any symmetric monoidal 3-category. There is furthermore a correspondence between algebraic structures on tensor categories and homotopy fixed point structures, which in turn provide structured field theories; we describe the expected connection between pivotal tensor categories and combed fixed point structures, and between spherical tensor categories and oriented fixed point structures.
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UNVERDICTED 4representative citing papers
A symmetry-extension construction of an anomalous 4d Z_{N_c}-gauge TQFT cancels the SM mixed anomaly and selects N_c = N_f = 3 as the unique odd-color solution.
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Authors introduce a TFT-based framework for finite topological symmetries in QFT, including gauging, condensation defects, and duality defects, with an appendix on finite homotopy theories.
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On the SymTFTs of Finite Non-Abelian Symmetries
Constructs BF-like 3D SymTFT Lagrangians for finite non-Abelian groups presented as extensions, yielding surface-attaching non-genuine line operators and Drinfeld-center fusion rules.
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Fermion Families and Pontryagin Class: Topological Field Theory via Colour Symmetry Extension
A symmetry-extension construction of an anomalous 4d Z_{N_c}-gauge TQFT cancels the SM mixed anomaly and selects N_c = N_f = 3 as the unique odd-color solution.
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Frobenius Algebras and Dual Bimodules in Monoidal 2-Categories
Explicit construction of dual bimodules from Frobenius algebras in monoidal 2-categories, with promotion of coherent duals and proof that special Frobenius algebras in 2Vect are rigid.
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Topological symmetry in quantum field theory
Authors introduce a TFT-based framework for finite topological symmetries in QFT, including gauging, condensation defects, and duality defects, with an appendix on finite homotopy theories.