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This joint project in the field of modern problems in theoretical and mathematical physics is aimed at the development of supersymmetry, quantum groups and integral models, and applications to condensed matter and elementary particle physics.
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results
The Munich group has worked in the field of Hopf algebras.
Quantum grous and their comodules are structures based on a non-commutative geometry and provide informations about non-commutative differential geometry. First the non-commutative spaces such as the Euclidean and Minkowski quantum spaces have been constructed. Then the manifold on which they act can be defined as the Hilbertspace representation of these systems. At last the investigation of the geometry on the algebra and on the manifold was begun.
The group of Prof. Filippov in Dubna has worked on deformed symmetries and integrable models.
Systematic investigation of discrete and Lie-algebraic symmetries of integrable systems, as well as explicit construction of new families of them, has been performed by A. Leznov. A new class of integrable mappings was studied, explicit presentation for the corresponding (1+2) integrable systems was given, and their soliton-like solutions were described. Moreover, the groups in Dubna have worked on the self-dual (super)gauge and (super)gravity theories in the twistor-harmonic approach. The charged hypermultiplet low-energy effective action in the Coulomb branch of the 4D, N=2 gauge theory was computed by using the harmonic superspace approach. The unique leading contribution was found to be given by the harmonic-analytic Lagrangian of the fourth order in the hypermultiplet superfields, with the induced coupling constant being proportional to central charges of N=2 SUSY algebra. The central charges are identified with the Cartan generators of the internal symmetry, and they give BPS masses to the hypermultiplets. Simultaneously, non-trivial scalar potentials are produced. The analysis was extended to a more general situation with non-vanishing Fayet-Iliopoulos (FI) terms. The perturbatively-induced Taub-NUT self-coupling in the Coulomb branch was found to be stable against adding the FI term, whereas the non-perturbatively generated (Eguchi-Hanson-type) hypermultiplet self-interaction was proposed for the Higgs branch.
The main activity of the Kharkhov group was directed to membrane models.
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