Skip to main content
European Commission logo print header
Contenu archivé le 2022-12-23

Low dimensional integrable models and their applications in field theory and statistical physics

Objectif

The project is devoted to development of the theory of low-dimensional integrable models.

The principal goals of the project are:
1) further development of the technique of computation of correlation functions and form-factors;
2) investigation of quantum symmetries of integrable models. The project will be undertaken by the four teams: from Yerevan Physics Institute (Yerevan, Armenia), Steklov Mathematics Institute and Physics Department of St.Petersburg University (St.Petersburg Russia), Institute for Theoretical Physics, Free University of Berlin (Berlin, Germany) and Laboratory of Particle Physics (Annecy-le-Vieux, France). Members of these teams work on various topics in the conformal field theory, the form-factor program, massive integrable models, quantum groups and W-algebras. The teams will collaborate on the form-factor program (Berlin and Yerevan), the dynamical symmetries of off-critical models (Annecy-le-Vieux and Yerevan), applications of the quantum groups (Annecy-le-Vieux and St.Petersburg) characters of conformal models (Berlin and St.Petersburg).

During the project implementation the following investigations will be carried out:
new representations of multi-point form-factors for various operators in the quantum sine-Gordon theory will be constructed;
various two-point correlation functions in the sine-Gordon and massive Thirring models will be calculated numerically;
form-factors related to various affine Toda field theories and the expectation values of exponential fields in the super-symmetric sine-Gordon and perturbed super-symmetric minimal models will be computed;
integral representations for correlation functions of the WZNW on a torus will be derived and their generalization to higher genus Riemann surfaces will be considered;
be the ansatz solution of Gaudin magnets corresponding to the exceptional Lie algebras will be obtained;
vertex type elliptic generalization of the KZ equation will be constructed and solved, and its connection with the elliptic Gaudin magnet will be investigated;
correlation functions of spin chains with non-periodic boundary conditions at the free fermion points will be calculated;
a q-deformation of the super-symmetric Virasoro algebra will be constructed and its bosonization at higher levels will be developed;
extensions of Wq,p(sl(n)) algebra will be investigated;
fermionic sum forms and product forms of characters for super-symmetric conformal models will be investigated;
twisting elements for finite-dimensional quantum algebras and super-algebras of low rank will be obtained and changes of physical characteristics in models related by these twists will be investigated;
transformations of dual Hopf algebras generated by twisting of original quasi-triangular Hopf algebras will be studied;
integrable deformations of the spherical top associated with outer automorphisms of the Lie algebra e(3,C) will be constructed;
non-canonical Sturm transformations for the Toda lattices and the Stackel systems will be developed;
generalizations of the Stackel systems related to the covering of hyper-elliptic curves will be studied;
representations of the Weyl algebras arising in 1+1 dimensional lattice models will be investigated and their connection to the Tomita theory of modular algebras will be considered;
lattice evolution operators for models related to higher rank quantum algebras will be constructed.

Appel à propositions

Data not available

Régime de financement

Data not available

Coordinateur

Freie Universität Berlin
Contribution de l’UE
Aucune donnée
Adresse
14 arnimallee
14195 Berlin
Allemagne

Voir sur la carte

Coût total
Aucune donnée

Participants (3)