Conformal quantum field theory

Project funded by Swedish Research Council (Project grant), grant 2009-03993_VR. Participating organisations named by the source: Karlstad University. Funded amount: SEK 1,755,000, as stated by the source. Runs 2010-01-01 to 2012-12-31. Keywords: Oklassificerat, Unclassified. Source: OpenAIRE Graph, from the funder's project data (collected by OpenAIRE on 2025-12-05); national funding data, not CORDIS. Abstract given by the source: A rigorous foundation of CFT - two-dimensional conformal quantum field theory - is sought that, unlike existing formulations, applies not only to rational CFT, but also to a wide class of nonrational models. Alongside, open problems in rational CFT will also be explored. The emphasis is on model-independent issues, though applications to specific models are envisaged as well. Relevant mathematical tools range from representation theory (of vertex algebras, of Artin algebras, and of quivers) to the topology of three-manifolds and to derived categories. The symmetries of a CFT are encoded in a vertex algebra V, coming with a category C of V-modules. In rational CFT this category is semisimple, and the basic further structure specifying a model is a Frobenius algebra in C. Given that algebra one can compute all correlation functions of the theory on any world sheet. The construction relies heavily on a three-dimensional topological field theory associated with C. Extending this approach to nonrational CFT, for which C is not semisimple and thus not modular, will require e.g. to determine which types of V-modules are admissible, to generalize the concept of Frobenius algebra in a way that preserves Morita invariance, and to apply tools from 3-d topology which do not suppose C to be modular. The project aims at making progress on all these issues. The problems of rational CFT that will be studied include in particular aspects of defect lines and of permutation orbifolds.

Original source.

Source: OpenAIRE Graph: projects of national funders, OpenAIRE, from the project data of Swedish Research Council. Retrieved 2026-10-28. Licence: Creative Commons Attribution 4.0 (OpenAIRE Graph). Selected metadata, adapted presentation; the publisher's record is authoritative. No endorsement by the source is implied. Licence: Creative Commons Attribution 4.0 (CC BY 4.0).

AI-assisted summary: The project 'Conformal quantum field theory' is funded by the Swedish Research Council with a grant of SEK 1,755,000, running from January 1, 2010, to December 31, 2012, at Karlstad University. It aims to establish a rigorous foundation for two-dimensional conformal quantum field theory. Suggested technology pillar: simulation. Generated by AI from the public source text; it may contain errors and the original source is authoritative.