The TFT construction of finite rigid CFTsOberseminar Darstellungstheorie

by Aaron Hofer (MPI)

Friday Jun 5, 2026, 2:15 PM → 3:15 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Even though two-dimensional conformal field theories have been studied by physicists and mathematicians for decades, a rigorous construction, in the form of a complete set of consistent correlation functions, still remains elusive for a large class of theories. Instead of tackling this construction problem directly, the situation becomes more tractable by splitting it into a complex-analytic/algebro-geometric and a purely algebraic/topological part. For the class of so-called rational CFTs the work of Fuchs, Runkel, and Schweigert completely solved the second part over twenty years ago, using the three dimensional topological field theories of Reshetikhin and Turaev.
In this talk, I will review the FRS construction and explain how it can be generalised to so-called finite rigid CFTs using the non-semisimple 3d TFTs of De Renzi, Gainutdinov, Geer, Patureau-Mirand, and Runkel. Moreover, I will illustrate how this construction can be used to obtain interesting algebras in non-semisimple modular tensor categories, and prove some of their properties purely topologically.