Introduces a graphical calculus for twisted pivotal categories and proves that associated string net modules on surfaces form an oriented categorified 2-TQFT independent of the Morse function, with analysis of vanishing on the 2-sphere linked to finite tensor categories.
Lyubashenko,Invariants of three manifolds and projective representations of mapping – 50 – class groups via quantum groups at roots of unity,Commun
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abstract
An example of a finite dimensional factorizable ribbon Hopf C-algebra is given by a quotient H=u_q(g) of the quantized universal enveloping algebra U_q(g) at a root of unity q of odd degree. The mapping class group M_{g,1} of a surface of genus g with one hole projectively acts by automorphisms in the H-module H^{*\otimes g}, if H^* is endowed with the coadjoint H-module structure. There exists a projective representation of the mapping class group M_{g,n} of a surface of genus g with n holes labelled by finite dimensional H-modules X_1,...,X_n in the vector space Hom_H(X_1\otimes...\otimes X_n,H^{*\otimes g}). An invariant of closed oriented 3-manifolds is constructed. Modifications of these constructions for a class of ribbon Hopf algebras satisfying weaker conditions than factorizability (including most of u_q(g) at roots of unity q of even degree) are described. The results are motivated by CFT.
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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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String nets for twisted pivotal categories
Introduces a graphical calculus for twisted pivotal categories and proves that associated string net modules on surfaces form an oriented categorified 2-TQFT independent of the Morse function, with analysis of vanishing on the 2-sphere linked to finite tensor categories.
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Candidate Gaugings of Categorical Continuous Symmetry
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.