Exactly solvable conformal field theories

Understand

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 $O(n)$, Potts and $PSU(n)$ 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.