Analytic bootstrap at large spin (1502.01437v6)

Abstract: We use analytic conformal bootstrap methods to determine the anomalous dimensions and OPE coefficients for large spin operators in general conformal field theories in four dimensions containing a scalar operator of conformal dimension $\Delta_\phi$. It is known that such theories will contain an infinite sequence of large spin operators with twists approaching $2\Delta_\phi+2n$ for each integer $n$. By considering the case where such operators are separated by a twist gap from other operators at large spin, we analytically determine the $n$, $\Delta_\phi$ dependence of the anomalous dimensions. We find that for all $n$, the anomalous dimensions are negative for $\Delta_\phi$ satisfying the unitarity bound. We further compute the first subleading correction at large spin and show that it becomes universal for large twist. In the limit when $n$ is large, we find exact agreement with the AdS/CFT prediction corresponding to the Eikonal limit of a 2-2 scattering with dominant graviton exchange.