Bootstrapping 2D CFTs in the semiclassical limit

We study two-dimensional conformal field theories in the semiclassical limit. in this limit, the four-point function is dominated by intermediate primaries of particular weights along with their descendants, and the crossing equations simplify drastically. for a four-point function receiving sufficiently small contributions from the light primaries, the structure constants involving heavy primaries follow a universal formula. applying our results to the four-point function of the $$ {mathbb{z}}_2 $$ twist field in the symmetric product orbifold, we produce the hellerman bound and the logarithmically corrected cardy formula that is valid for h ≥ c/12.