The S-matrix Bootstrap II: Two Dimensional Amplitudes

TL;DR

This paper derives rigorous bounds on the S-matrix in 1+1 dimensional quantum field theories using crossing symmetry and unitarity, identifying integrable theories that saturate these bounds and connecting to numerical bootstrap results.

Contribution

It establishes analytical bounds on cubic couplings in 1+1D QFTs and links these to integrable models and numerical bootstrap findings.

Findings

Analytic bounds on cubic couplings in 1+1D QFTs.

Identification of integrable theories saturating bounds.

Agreement between analytic and numerical bootstrap results.

Abstract

We consider constraints on the S-matrix of any gapped, Lorentz invariant quantum field theory in 1 + 1 dimensions due to crossing symmetry and unitarity. In this way we establish rigorous bounds on the cubic couplings of a given theory with a fixed mass spectrum. In special cases we identify interesting integrable theories saturating these bounds. Our analytic bounds match precisely with numerical bounds obtained in a companion paper where we consider massive QFT in an AdS box and study boundary correlators using the technology of the conformal bootstrap.