The S-matrix Bootstrap I: QFT in AdS

TL;DR

This paper introduces a novel approach to studying massive QFTs by leveraging conformal bootstrap methods in hyperbolic space, connecting boundary correlators to flat-space scattering amplitudes, and deriving bounds on cubic couplings.

Contribution

It proposes a new strategy to analyze flat-space QFTs via boundary correlators in hyperbolic space, bridging conformal bootstrap and S-matrix techniques.

Findings

Derived universal bounds on cubic couplings in 2D QFTs.

Numerical results match analytic bounds from S-matrix bootstrap.

Established a connection between boundary correlators and flat-space scattering amplitudes.

Abstract

We propose a strategy to study massive Quantum Field Theory (QFT) using conformal bootstrap methods. The idea is to consider QFT in hyperbolic space and study correlation functions of its boundary operators. We show that these are solutions of the crossing equations in one lower dimension. By sending the curvature radius of the background hyperbolic space to infinity we expect to recover flat-space physics. We explain that this regime corresponds to large scaling dimensions of the boundary operators, and discuss how to obtain the flat-space scattering amplitudes from the corresponding limit of the boundary correlators. We implement this strategy to obtain universal bounds on the strength of cubic couplings in 2D flat-space QFTs using 1D conformal bootstrap techniques. Our numerical results match precisely the analytic bounds obtained in our companion paper using S-matrix bootstrap techniques.