AdS/CFT unitarity at higher loops: high-energy string scattering

David Meltzer

doi:10.1007/jhep05(2020)133

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.

Highlights

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
The physical motivation for studying the CFT Regge limit is manifest in AdS, where it is dual to high-energy scattering at fixed impact parameter [16,17,18]
After resumming the leading trajectory, we find the Regge limit is controlled by the exchange of an operator with non-integer spin, which is known as the “Pomeron” or reggeized graviton [14, 15, 19, 20, 30]

Summary

Introduction

The physical motivation for studying the CFT Regge limit is manifest in AdS, where it is dual to high-energy scattering at fixed impact parameter [16,17,18]. In this limit, the dominant contribution at tree-level in 1/N comes from the leading Regge trajectory, or the set of operators with the lowest dimension for each even-spin [19, 20]. We demonstrate how tidal excitations, an inelastic effect dual to new double-trace exchanges at one-loop, are suppressed when we take ∆gap large

Objectives

Discussion

Conclusion