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3-Dimensional TQFTs From Non-Semisimple Modular Categories

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arxiv 1912.02063 v3 pith:DBBMEIGX submitted 2019-12-04 math.GT hep-thmath.QA

Marco De Renzi , Azat M. Gainutdinov , Nathan Geer , Bertrand Patureau-Mirand , Ingo Runkel This is my paper
classification math.GThep-thmath.QA
keywords categoriesnon-semisimplecominginvariantslyubashenkomodulartqftsadditional
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We use modified traces to renormalize Lyubashenko's closed 3-manifold invariants coming from twist non-degenerate finite unimodular ribbon categories. Our construction produces new topological invariants which we upgrade to 2+1-TQFTs under the additional assumption of factorizability. The resulting functors provide monoidal extensions of Lyubashenko's mapping class group representations, as discussed in arXiv:2010.14852. This general framework encompasses important examples of non-semisimple modular categories coming from the representation theory of quasi-Hopf algebras, which were left out of previous non-semisimple TQFT constructions.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Defects in skein theory and TQFT

    math.QA 2026-06 unverdicted novelty 7.0 of 10

    Defines defect skein modules for 3-manifolds with line and point defects and proves they match state spaces of defect Reshetikhin-Turaev TQFT for semisimple data.

  2. Candidate Gaugings of Categorical Continuous Symmetry

    hep-th 2026-04 unverdicted novelty 6.0 of 10

    Candidate modular invariants and gaugings for continuous G-symmetries with anomaly k are obtained from +1 eigenspaces of semiclassical modular kernels in a BF+kCS SymTFT model.

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