The statistics of spin for CFTs

I will discuss universal behavior of CFT data at high energies. In particular I will discuss universal formulas for both the entropy and the three-point-functions of local operators for d-dimensional CFT (d>2) as a function of energy and spin, using a technique called thermal effective field theory. This can be thought of as a higher-dimensional version of Cardy's formula for 2d CFTs. I will also discuss holographic interpretations of this result. Based on work to appear with J. Lee, H. Ooguri, and D. Simmons-Duffin.