Adding flavour to the S-matrix bootstrap

TL;DR

This paper investigates the bounds of scattering amplitudes in 1+1D quantum field theories with O(N) symmetry, revealing connections to known integrable models and discovering complex, exotic S-matrix structures beyond integrability.

Contribution

It introduces a novel extremization approach for scattering couplings, uncovering new S-matrix solutions with rich resonance structures and exploring their relation to integrable and non-integrable theories.

Findings

Known integrable models are recovered at bounds.

Discovered exotic S-matrices with infinite resonances.

Identified potential links to realistic theories with particle production.

Abstract

We explore the S-matrices of gapped, unitary, Lorentz invariant quantum field theories with a global O($N$) symmetry in 1+1 dimensions. We extremize various cubic and quartic couplings in the two-to-two scattering amplitudes of vector particles. Saturating these bounds, we encounter known integrable models with O($N$) symmetry such as the O($N$) Gross-Neveu and non-linear sigma models and the scattering of kinks in the sine-Gordon model. We also considered more general mass spectra for which we move away from the integrable realm. In this regime we find (numerically, through a large N analysis and sometimes even analytically) that the S-matrices saturating the various coupling bounds have an extremely rich structure exhibiting infinite resonances and virtual states in the various kinematical sheets. They are rather exotic in that they admit no particle production yet they do not obey Yang-Baxter equations. We discuss their physical (ir)relevance and speculate, based on some preliminary numerics, that they might be close to more realistic realistic theories with particle production.