Mathematical Physics

Recent work of Bonifacio-Hinterbichler, Bonifacio, and Kravchuk-Mazáč-Pal introduced an analogy at the level of representation theory between conformal field theories and hyperbolic surfaces. In the spectral theory of hyperbolic surfaces, there are analogs of scaling dimensions of local operators and OPE coefficients, and these numbers obey an analog of crossing symmetry. The conformal bootstrap can thus be adapted to constrain these numbers. How strong are the resulting constraints? The main result of this talk is that they are complete constraints: every solution to the crossing equations must come from a hyperbolic surface (this is a rigorous theorem).