School/Workshop on Integrable Models: From Quantum Spin Chains
    and Vertex Models to AdS/CFT

July 2-14, 2018

São Paulo, Brazil



Integrability has become a tool of choice in studying classical and quantum interacting systems, being one of the few non-perturbative methods available. For a long time it was restricted to one dimensional systems, and as such it found numerous applications in low-dimensional systems in condensed matter physics, and more generally in statistical physics. From its beginning, integrability is deeply intertwined with mathematics, from which it draws inspiration and rigour. More recently, integrability found surprising applications in a new approach to quantum gauge theories, with new ideas arising from dualities between gauge and string theory. Through the impressive and widely recognised successes in the calculation of anomalous dimensions, scattering amplitudes and correlation functions in planar N=4 super-Yang-Mills theory on the one hand, and the exact determination of the low-energy physics of N=2 super-Yang-Mills theories on the other hand, a new perspective is emerging on gauge theory viewed as an integrable system.

This program aims at bringing together young researchers and specialists in integrability from statistical physics, condensed matter physics, gauge and string theory and mathematics. The purpose is to provide the young researchers with the necessary background for working in these rapidly evolving fields, and to stimulate cross-fertilization of different research areas.

The two-week program will start with a school followed by a workshop. The school is probably the most important component of the program. Experts from high-energy integrability will lecture aiming at an audience of cond-mat/stat-mech integrabilists and vice versa. So it should be a great opportunity for learning the different approaches. The workshop will be quite relaxed with about 2 talks per day, one on high-energy and the other on cond-mat/stat-mech, again aiming at stimulating interactions between the two communities.

This ICTP-SAIFR program is part of a coordinated set of programs starting with a portion in Stockholm in Nordita from May 14 to June 8, 2018, followed by a two-week program in Natal at the IIP from June 18 June – 29 of June right before this Sao Paulo program. Note that most flights to Natal pass by Sao Paulo anyways so we hope many people will coordinate and come for both programs. There is no registration fee for the program in São Paulo and limited funds are available for travel and local expenses. We hope to see you in Sao Paulo (and Stockholm and Natal as well) for an exciting interdisciplinary meeting.


  • Vladimir Korepin (State University of New York at Stony Brook, USA)
  • Giuliano Ribeiro (UFSCar, Brazil)
  • Didina Serban (IPhT-Saclay, France)
  • Pedro Vieira (ICTP-SAIFR/IFT-UNESP, Brazil & Perimeter Institute, Canada)

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Lecturers & Speakers

School Lecturers:

  • Shota Komatsu (IAS-Princeton, USA): Integrability in four-dimensional gauge theories: beyond spectral problem
  • Vladimir Korepin (State University of New York at Stony Brook, USA): Quantum Inverse Scattering Method

The lectures will start with Lax representation and Hamiltonian structure of classical differential equations of evolutionary type [examples are non-linear Schroedinger and  sine-Gordon]. The lectures will proceed to quantum inverse scattering matrix and algebraic Bethe Ansatz. Spin chains and Hubbard model  also will be mentioned as well as  quantum determinants and Yangians.


1) Quantum Inverse Scattering Method and Correlation Functions; V. Korepin

2) An Introduction to Yangian Symmetries

3) The Yangian symmetry of the Hubbard Model

4) A lattice model related to the nonlinear Schroedinger equation

5) The one-dimensional Hubbard model

  • Márcio José Martins (UFSCar, Brazil): Integrable Lattice Models and Algebraic Geometry
  • Konstantin Zarembo (NORDITA, Sweden): Origins of AdS/CFT integrability
The lectures will introduce the AdS/CFT duality between gauge fields in four dimensions and string theory on the Anti-de-Sitter background, alongside evidence for integrability of the AdS/CFT system. The basic tools of the AdS/CFT integrability, mostly applied to the spectral problem, and underlying symmetry principles will be presented at a non-technical level.
1. Introduction of the AdS/CFT correspondence:
2. Collection of reviews on the AdS/CFT integrability:
3. A review of the Quantum Spectral Curve method (the most advanced spectral tool in the AdS/CFT integrability):
4. A review of integrability in sigma-models:


Workshop Speakers:

  • Frank Coronado (Perimeter Institute, Canada): The simplest four-point correlator in planar N=4 SYM
  • Patrick Dorey (Durham University, UK)
  • Vladimir Kazakov (Laboratoire de Physique Théorique École Normale Supérieure, France): Conformal fishnet theory
  • Ivan Kostov (Université Paris Saclay, France): Boundary TBA, trees and loops
  • Luis M. Kruckzenski (Purdue U., USA): The S-matrix Bootstrap for the 2d O(N) bosonic model
  • Ivar Lyberg (IIP-UFRN, Brazil): The six vertex model with various boundary conditions
  • Pramod Padmanabhan (Institute for Basic Science – Daejeon, South Korea): Semigroup Quantum Spin Chains
  • Alexander B. Zamolodchikov (Rutgers University, USA): ${\bar T}$ flow, partition function, and universal contact terms.
  • Deliang Zhong (Le Laboratoire de Physique Théorique de l’Ecole Normale Supérieure, France): Continuum limit of fishnet graphs and AdS sigma model

Short talks:

  • Gwenaël Ferrando (l’Ecole Normale Supérieure, France): Conformal dimensions in the fishnet theory
  • Rodrigo Alves Pimenta (UFSCar, Brazil): A tale of two Bethe ansätze
  • Tarun Sharma (University of the Witwatersrand, South Africa): Hint of Integrability in Chern Simons vector models



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SchoolWorkshop on Integrable Models


School/Workshop program:  PDF updated on July 11, 2018

Videos & Notes

Integrability in four-dimensional gauge theories: beyond spectral problem: Prof. Shota Komatsu

Lecture 1 Notes
Lecture 2 Notes
Lecture 3 Notes
Lecture 4 Notes
Lecture 5 Notes
Additional Material

Quantum Inverse Scattering Method: Prof. Vladimir Korepin

Lecture 1 Notes
Lecture 2 Notes
Lecture 3 Notes
Lecture 4 Notes
Lecture 5 Notes
Additional Material

Integrable Lattice Models and Algebraic Geometry: Prof. Márcio José Martins

Lecture 1 Notes
Lecture 2 Notes
Lecture 3 Part 1 and Part 2 Notes
Lecture 4 Notes
Lecture 5 Notes
Additional Material

Konstantin Zarembo: Prof. Origins of AdS/CFT integrability

Lecture 1 Notes
Lecture 2
Lecture 3 Part 1 and Part 2
Lecture 4 Part 1 and Part 2
Lecture 5
Additional Material


Additional Information