Unitarity Methods in AdS/CFT

TL;DR

This paper introduces a unitarity-based framework for calculating loop-level AdS scattering amplitudes, linking bulk and boundary perspectives, and providing efficient computational techniques for non-planar CFT correlators.

Contribution

It develops a systematic unitarity method for AdS amplitudes, connecting cutting and gluing techniques with holographic unitarity, and applies it to various one-loop diagrams.

Findings

Computed cuts of scalar bubble, triangle, and box diagrams.

Established a map between bulk cutting-gluing and holographic unitarity.

Analyzed four-point and five-point amplitudes with new efficiency.

Abstract

We develop a systematic unitarity method for loop-level AdS scattering amplitudes, dual to non-planar CFT correlators, from both bulk and boundary perspectives. We identify cut operators acting on bulk amplitudes that put virtual lines on shell, and show how the conformal partial wave decomposition of the amplitudes may be efficiently computed by gluing lower-loop amplitudes. A central role is played by the double discontinuity of the amplitude, which has a direct relation to these cuts. We then exhibit a precise, intuitive map between the diagrammatic approach in the bulk using cutting and gluing, and the algebraic, holographic unitarity method of arXiv:1612.03891 that constructs the non-planar correlator from planar CFT data. Our analysis focuses mostly on four-point, one-loop diagrams -- we compute cuts of the scalar bubble, triangle and box, as well as some one-particle reducible diagrams -- in addition to the five-point tree and four-point double-ladder. Analogies with S-matrix unitarity methods are drawn throughout.