Regge in Wonderland
We study the asymptotic behavior of large-spin operators in conformal field theories by placing the theory on a pp-wave background. In this setting, three-point coefficients involving two large-spin operators and a light operator are mapped to thermal one-point functions on the pp-wave. We predict these one-point functions in the two complementary regimes of high- and low-temperature respectively, corresponding to a limit in which the twist scales with an appropriate power of the spin and the spin is parametrically larger than the twist, respectively. In particular, at high temperature we derive their asymptotic behavior using thermal effective field theory while at low temperature we obtain results that can be matched directly to predictions from the analytic bootstrap. We test these general results in free scalar theories. Finally, we solve the large-$N$ $\mathrm{O}(N)$ model numerically on the pp-wave, finding agreement with our predictions for both the one-point function and the free energy in the high- and low-temperature regimes.