Adding flavour to the S-matrix bootstrap

Lucía Córdova (1) , Pedro Vieira

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681

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 theories with particle production.

Mots clés: Field Theories in Lower Dimensions; Integrable Field Theories; Nonperturbative Effects; Scattering Amplitudes; sigma model: nonlinear; model: integrability; invariance: Lorentz; kink: scattering; S-matrix; scattering amplitude; field theory; sine-Gordon model; vector particle; expansion 1/N; mass spectrum; bootstrap; unitarity; flavor

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Lucía Córdova, Pedro Vieira. Adding flavour to the S-matrix bootstrap. Journal of High Energy Physics, 2018, 12, pp.063. ⟨10.1007/JHEP12(2018)063⟩. ⟨hal-01815169⟩