3-Dimensional TQFTs from Non-Semisimple Modular Categories
| Autor: | Marco De Renzi, Azat M. Gainutdinov, Nathan Geer, Bertrand Patureau-Mirand, Ingo Runkel |
|---|---|
| Přispěvatelé: | Laboratoire de Mathématiques et Physique Théorique (LMPT), Centre National de la Recherche Scientifique (CNRS)-Université de Tours, Laboratoire de mathématiques de Brest (LM), Université de Brest (UBO)-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS), Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO), Université de Tours-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
High Energy Physics - Theory
General Mathematics knot theory [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] FOS: Physical sciences General Physics and Astronomy Geometric Topology (math.GT) algebra field theory: topological group: representation Mathematics - Geometric Topology Automatic Keywords High Energy Physics - Theory (hep-th) category: modular Mathematics::Quantum Algebra Mathematics::Category Theory Mathematics - Quantum Algebra twist FOS: Mathematics Quantum Algebra (math.QA) upgrade unimodular |
| Popis: | 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. 49 pages; v3: added pictures and references |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|