The TFT construction of finite rigid CFTsMPIM

by Aaron Hofer (MPIM)

Monday Jul 6, 2026, 2:00 PM → 3:00 PM Europe/Berlin

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

MPIM Topology Seminar

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 the 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 focus on the second part of this problem. More specifically, I will review the main ideas of the FRS construction and explain how generalising it to so-called finite rigid CFTs using the non-semisimple 3d TFTs of De Renzi, Gainutdinov, Geer, Patureau-Mirand, and Runkel.