Adding flavour to the S-matrix bootstrap

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.

37 pages, 17 figures; new Yang Baxter solution identified with S-matrix previously found by Hortacsu, Schroer and Thun; references added; signs in equations 13 and 35 corrected

References in corpus (4)

• On space of integrable quantum field theories
• A note on the S-matrix bootstrap for the 2d O(N) bosonic model
• S-matrix bootstrap for resonances
• Inelastic scattering and elastic amplitude in Ising field theory in a weak magnetic field at T>T_c. Perturbative analysis

Cited by in corpus (29)

• A Study of Quantum Field Theories in AdS at Finite Coupling
• Bootstrapping QCD: the Lake, the Peninsula and the Kink
• Flux Tube S-matrix Bootstrap
• The S-matrix Bootstrap IV: Multiple Amplitudes
• Bootstrap for Lattice Yang-Mills theory
• Bootstrapping Pions at Large $N$
• Bootstrapping Massive Quantum Field Theories
• The O(N) S-matrix Monolith
• Dual S-matrix Bootstrap I: 2D Theory
• Distributions in CFT II. Minkowski Space
• S-matrix bootstrap in 3+1 dimensions: regularization and dual convex problem
• Rigorous bounds on the Analytic $S$-matrix
• SUSY S-matrix Bootstrap and Friends
• Towards Bootstrapping RG flows: Sine-Gordon in AdS
• Scattering from production in 2d
• Constraints on Sequential Discontinuities from the Geometry of On-shell Spaces
• Nonperturbative Bounds on Scattering of Massive Scalar Particles in $d\ge 2$
• Swampland Conditions for Higher Derivative Couplings from CFT
• EFT Asymptotics: the Growth of Operator Degeneracy
• Bootstrapping the $a$-anomaly in $4d$ QFTs
• Thermodynamic Bethe Ansatz past turning points: the (elliptic) sinh-Gordon model
• Two-particle spectrum of tensor multiplets coupled to $Ad{S}_3\times S^3$ gravity
• Bounds on photon scattering
• The R-matrix bootstrap for the 2d O(N) bosonic model with a boundary
• Bootstrapping 2d ${\varphi }^4$ Theory with Hamiltonian Truncation Data
• From conformal correlators to analytic S-matrices: CFT${}_1$/QFT${}_2$
• Strings from Almost Nothing
• Primal S-matrix bootstrap with dispersion relations
• A Large-$N$ Expansion for Minimum Bias