Analytic bootstrap at large spin

TL;DR

This paper uses analytic bootstrap techniques to determine the behavior of large spin operators in four-dimensional conformal field theories, revealing universal corrections and agreement with AdS/CFT predictions.

Contribution

It analytically computes anomalous dimensions and OPE coefficients for large spin operators, including subleading corrections, in 4D CFTs with a scalar operator, extending understanding of their structure.

Findings

Anomalous dimensions are negative for all n within the unitarity bound.

First subleading correction at large spin is universal for large twist.

Results agree with AdS/CFT Eikonal limit predictions.

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.