Since the 1980s, it has been well known that there is a close relationship between two-dimensional conformal field theories and three-dimensional topological field theories. This CFT/TFT correspondence provides a tractable example of holography as well as a first example of the symmetry TFT framework.

The Fuchs-Runkel-Schweigert construction is a mathematically precise incarnation of this correspondence and provides a rigorous construction of correlators for rational CFTs using 3D TFTs of Reshetikhin-Turaev type. In this talk, I will review the FRS construction and explain how it can be generalized to non-rational CFTs using the non-semisimple 3D TFTs of De Renzi, Gainutdinov, Geer, Patureau-Mirand, and Runkel.