AdS/CFT Unitarity at Higher Loops: High-Energy String Scattering

TL;DR

This paper investigates the unitarity of AdS/CFT at higher loops by analyzing high-energy string scattering in large N, 4D CFTs, providing evidence that their bulk amplitudes align with string theory predictions to all orders.

Contribution

It develops a unitarity-based bootstrap method to compute all-order corrections in AdS/CFT, demonstrating the exponentiation of Pomeron exchange in the 1/N expansion.

Findings

Bulk scattering amplitudes match string theory predictions.

Pomeron exchange exponentiates in the 1/N expansion.

Tree-level results extend to all orders under certain conditions.

Abstract

What is the space of weakly-coupled, gravitational theories which contain massive, higher-spin particles? This class of theories is highly constrained and it is conjectured their ultraviolet completion must be string theory. We provide more evidence for this conjecture by studying the Regge limit in large $N$, $4d$ CFTs with single-trace operators of unbounded spin. We show that in the Regge limit, these theories have bulk scattering amplitudes which are consistent with the string theory prediction to all orders in $1/N$ for large, but finite, coupling. In the language of Regge theory, we show Pomeron exchange naturally exponentiates in the $1/N$ expansion. To do this, we solve the bootstrap equations at tree-level and then use the Lorentzian inversion formula to find the one-loop correlator in the Regge limit. This is a unitarity method for AdS/CFT which can be repeated iteratively to make all orders statements. We also explain under what conditions the tree-level result exponentiates in the $1/N$ expansion at arbitrary coupling. Finally, we comment on further inelastic effects and show they give subleading contributions at large coupling. As a consistency check, we recover results from bulk Einstein gravity in the limit where all higher-spin particles decouple.