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  • 1.
    Fuchs, Jürgen
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013).
    Schweigert, Christoph
    Hamburg University.
    Consistent systems of correlators in non-semisimple conformal field theory2017In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 307, p. 598-639Article in journal (Refereed)
    Abstract [en]

    Based on the modular functor associated with a -- not necessarily semisimple -- finite non-degenerate ribbon category D, we present a definition of a consistent system of bulk field correlators for a conformal field theory which comprises invariance under mapping class group actions and compatibility with the sewing of surfaces. We show that when restricting to surfaces of genus zero such systems are in bijection with commutative symmetric Frobenius algebras in D, while for surfaces of any genus they are in bijection with modular Frobenius algebras in D. This provides additional insight into structures familiar from rational conformal field theories and extends them to rigid logarithmic conformal field theories.

  • 2.
    Fuchs, Jürgen
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013).
    Schweigert, Christoph
    Hamburg University.
    Stigner, Carl
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013).
    Higher genus mapping class group invariants from factorizable Hopf algebras2014In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 250, p. 285-319Article in journal (Refereed)
    Abstract [en]

    Lyubashenko's construction associates representations of mapping class groups Map_{g,n} of Riemann surfaces of any genus g with any number n of holes to a factorizable ribbon category. We consider this construction as applied to the category of bimodules over a finite-dimensional factorizable ribbon Hopf algebra H. For any such Hopf algebra we find an invariant of Map_{g,n} for all values of g and n. More generally, we obtain such invariants for any pair (H,omega), where omega is a ribbon automorphism of H. Our results are motivated by the quest to understand correlation functions of bulk fields in two-dimensional conformal field theories with chiral algebras that are not necessarily semisimple, so-called logarithmic conformal field theories.

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