# Conformal Bootstrap in the Regge Limit

## TL;DR

This paper analytically solves conformal bootstrap equations in the Regge limit for large N theories, revealing how crossing symmetry constrains operator dimensions, correlators, and their holographic duals, with implications for chaos and AdS/CFT correspondence.

## Contribution

It provides an analytical framework for the Regge limit in large N conformal field theories, connecting bootstrap equations to AdS exchange diagrams and chaos bounds.

## Key findings

- Dominance of spin-2 exchanges in large N theories.
- Negative anomalous dimensions consistent with chaos bound.
- Reproduction of CEMZ constraints on three-point functions.

## Abstract

We analytically solve the conformal bootstrap equations in the Regge limit for large N conformal field theories. For theories with a parametrically large gap, the amplitude is dominated by spin-2 exchanges and we show how the crossing equations naturally lead to the construction of AdS exchange Witten diagrams. We also show how this is encoded in the anomalous dimensions of double-trace operators of large spin and large twist. We use the chaos bound to prove that the anomalous dimensions are negative. Extending these results to correlators containing two scalars and two conserved currents, we show how to reproduce the CEMZ constraint that the three-point function between two currents and one stress tensor only contains the structure given by Einstein-Maxwell theory in AdS, up to small corrections. Finally, we consider the case where operators of unbounded spin contribute to the Regge amplitude, whose net effect is captured by summing the leading Regge trajectory. We compute the resulting anomalous dimensions and corrections to OPE coefficients in the crossed channel and use the chaos bound to show that both are negative.