Lectures on S-matrices and Integrability

Abstract

In these notes we review the S-matrix theory in (1+1)-dimensional integrable models, focusing mainly on the relativistic case. Once the main definitions and physical properties are introduced, we discuss the factorization of scattering processes due to integrability. We then focus on the analytic properties of the two-particle scattering amplitude and illustrate the derivation of the S-matrices for all the possible bound states using the so-called bootstrap principle. General algebraic structures underlying the S-matrix theory and its relation with the form factors axioms are briefly mentioned. Finally, we discuss the S-matrices of sine-Gordon and SU(2), SU(3) chiral Gross-Neveu models. This is part of a collection of lecture notes for the Young Researchers Integrability School, organized by the GATIS network at Durham University on 6-10 July 2015.

52 pages, 13 figures; v2: minor corrections and references added, matching the published version

References in corpus (25)

• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
• Form factors in finite volume II:disconnected terms and finite temperature correlators
• Wrapping interactions at strong coupling -- the giant magnon
• The complete AdS_3 x S^3 x T^4 worldsheet S-matrix
• The Quantum Spectral Curve of the ABJM theory
• All-loop worldsheet S matrix for AdS_3 x S^3 x T^4
• Towards integrability for AdS3/CFT2
• The Bethe ansatz approach for factorizable centrally extended S-matrices
• Lectures on Yangian Symmetry
• Lectures on the Bethe Ansatz
• Introduction to the thermodynamic Bethe ansatz
• Massless Lüscher Terms and the Limitations of the AdS3 Asymptotic Bethe Ansatz
• Integrable S-matrices, massive and massless modes and the AdS_2 x S^2 superstring
• Finite size giant magnons in the SU(2) x SU(2) sector of AdS_4 x CP^3
• The ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathrm{S}}^3\times {\mathrm{S}}^1$ worldsheet S matrix
• The Form Factor Program: a Review and New Results - the Nested SU(N) Off-Shell Bethe Ansatz
• Exact form factors of the SU(N) Gross-Neveu model and 1/N expansion
• Fields, particles and universality in two dimensions
• The nested SU(N) off-shell Bethe ansatz and exact form factors
• The S-matrix algebra of the AdS2 X S2 superstring
• Fusion for the one-dimensional Hubbard model
• Seeing asymptotic freedom in an exact correlator of a large-$N$ matrix field theory
• Yang-Mills Theories as Deformations of Massive Integrable Models

Cited by in corpus (19)

• Lectures on Yangian Symmetry
• Lectures on the Bethe Ansatz
• Scattering into one-dimensional waveguides from a coherently-driven quantum-optical system
• Introduction to the thermodynamic Bethe ansatz
• An Integrability Primer for the Gauge-Gravity Correspondence: an Introduction
• The low-energy limit of AdS${}_3$/CFT${}_2$ and its TBA
• Lectures on Integrable Structures in Quantum Field Theory and Massive ODE/IM Correspondence
• Supersymmetric integrable theories from no particle production
• Resurgence in the Bi-Yang-Baxter Model
• Inelastic decay from integrability
• Hexagonalization of Fishnet integrals I: mirror excitations
• Perturbative renormalization of the $T\bar{T}$-deformed free massive Dirac fermion
• Nonlocal Symmetries and Factorized Scattering
• Majorana quanta, string scattering, curved spacetimes and the Riemann Hypothesis
• A study of integrable form factors in massless relativistic AdS_3
• From conformal correlators to analytic S-matrices: CFT${}_1$/QFT${}_2$
• Integrability structures in string theory
• Geometry of Massless Scattering in Integrable Superstring
• Tropical limit of matrix solitons and entwining Yang-Baxter maps