Integrable spin chains, statistical models on the lattice and integrable 2d field theories
Integrable spin chains are often used as lattice regularizations of integrable field theories, and they are particularly useful for non-unitary or non-compact theories, as they offer analytical control via the representation theory of quantum groups. Non-unitary quantum field theories in 1+1 dimensions appear naturally in the description of a variety of gapless systems of statistical mechanics, such as percolation and polymers, or quantum critical points separating the plateaux in 2+1-dimensional topological insulators. The loss of unitarity can be traced back to either weak non-locality, or averaging over disorder. Non-compact theories also appear in theories with disorder, or in the description of low-dimensional quantum gravity. An important effort is devoted to study boundary conditions which preserve integrability and /or conformality. Integrability is also used to build lattice regularizations of topological defects in two-dimensional conformal field theories, and to uncover new families of topological defects. Long-range integrable models are studied for their close relationship to conformal field theories and for their mathematical properties implementing lattice regularizations of current symmetry algebras. Computation of correlation functions in integrable field theories benefit of the new approaches to the Thermodynamical Bethe Ansatz that we are developing.

Correlation functions in four-dimensional integrable supersymmetric gauge theories
We focus on the planar limit of a maximally supersymmetric four-dimensional gauge theory (MSYM), which on the one hand can be viewed as a toy model for quantum chromodynamics, and on the other hand is dual to string theory in Anti-de Sitter space. While the spectral problem in this theory is in principle solved, computing correlators is a challenge that goes well beyond standard integrability techniques such as the Bethe Ansatz. We are developing other methods, using separation of variables for integrable spin chains, form-factor approach for integrable 2d field theories and the use of infinite-dimensional symmetry algebras. With these techniques were able to compute a particular correlation function in the planar N = 4 SYM theory with large charges for any value of the coupling constant. The associated object, called octagon form factor, is also appearing in the expression of various quantities associated to certain N = 2 super-conformal models and it is closely related to the celebrated Tracy-Widom distribution and its finite temperature generalization.
Other integrable deformations of the MSYM are useful to compute Feynman integrals, for example the so-called fishnet theory, corresponding to rectangular Feynman graphs. Correlation functions of this theory were shown to be Yangian invariant, and can be determined using integrability and matrix model techniques.
Scientific staff
Michel BAUER | |||
Michel BERGERE | |||
Jérémie BOUTTIER | |||
Philippe DI FRANCESCO | |||
Bertrand EYNARD | |||
Riccardo GUIDA | |||
Emmanuel GUITTER | |||
Jesper JACOBSEN * | |||
Ivan KOSTOV | |||
Grégoire MISGUICH | |||
Vincent PASQUIER | |||
Sylvain RIBAULT | |||
Hubert SALEUR | |||
Didina SERBAN |