2019/03/07 by Jürgen Fuchs, Christoph Schweigert
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Boundary (topology) #Boundary conformal field theory #Combinatorics #Computer science #Conformal field theory #Conformal map #Field (mathematics) #Functor #Geometry #Graph #Homotopy and Cohomology in Algebraic Topology #Logarithm #Mathematical analysis #Mathematics #Modular design #Neumann boundary condition #Physics #Pure mathematics #Theoretical physics #Vertex (graph theory) #hep-th
paper · pdf · doi:10.1002/prop.201910018
13 pages, Contribution to Proceedings of LMS/EPSRC Durham Symposium Higher Structures in M-Theory, August 2018
arxiv created 2019/03/07 · openalex publication_date 2019/05/15 · arxiv updated 2021/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract Logarithmic conformal field theories are based on vertex algebras with non‐semisimple representation categories. While examples of such theories have been known for more than 25 years, some crucial aspects of local logarithmic CFTs have been understood only recently, with the help of a description of conformal blocks by modular functors. We present some of these results, both about bulk fields and about boundary fields and boundary states. We also describe some recent progress towards a derived modular functor. This is a summary of work with Terry Gannon, Simon Lentner, Svea Mierach, Gregor Schaumann and Yorck Sommerhäuser.