Full Logarithmic Conformal Field theory - an Attempt at a Status Report

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.

13 pages, Contribution to Proceedings of LMS/EPSRC Durham Symposium Higher Structures in M-Theory, August 2018

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• Braided tensor categories of admissible modules for affine Lie algebras
• Bosonic Ghosts at $c=2$ as a Logarithmic CFT
• A modular invariant bulk theory for the c=0 triplet model
• Categorification and correlation functions in conformal field theory
• Open Strings On The Rindler Horizon
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Cited by in corpus (3)

• Algebraic structures in two-dimensional conformal field theory
• Character Vectors of Strongly Regular Vertex Operator Algebras
• The Cyclic and Modular Microcosm Principle in Quantum Topology