A Cardy Formula for Three-Point Coefficients: How the Black Hole Got its Spots

Understand

Modular covariance of torus one-point functions constrains the three point function coefficients of a two dimensional CFT.

• This leads to an asymptotic formula for the average value of light-heavy-heavy three point coefficients, generalizing Cardy's formula for the high energy density of states.
• The derivation uses certain asymptotic properties of one-point conformal blocks on the torus.
• Our asymptotic formula matches a dual AdS_3 computation of one point functions in a black hole background.