Exactly solvable conformal field theories
Year: 2026
Type: article
Abstract: We review 2d CFT in the bootstrap approach, and sketch the known exactly solvable CFTs with no extended chiral symmetry: Liouville theory, (generalized) minimal models, limits thereof, and loop CFTs, including the O(n) O ( n ) , Potts and PSU(n) P S U ( n ) CFTs. Exact solvability relies on local conformal symmetry, and on the existence of degenerate fields. We show how these assumptions constrain the spectrum and correlation functions. We discuss how crossing symmetry equations can be solved analytically and/or numerically, leading to analytic expressions for structure constants in terms of the double Gamma function. In the case of loop CFTs, we sketch the corresponding statistical models, and derive the relation between statistical and CFT variables. We review the resulting combinatorial description of correlation functions, and discuss what remains to be done for solving the CFTs.
Source: SciPost Physics Lecture Notes
Author: Sylvain Ribault
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4404988628