The main goal of the Project is to get further insights into the geometrical, group-theoretical and quantum structure of gauge theories with extended super-symmetry in their close intertwining relationships with string theory, theory of interacting higher spins, integrable models and non-commutative field theory. Fundamental properties of String/M-theory will be brought to light by studying the dualities and hidden symmetries of super-gravity and super-brane models, as well as flux compactifications. Higher-order alpha prime Dirac-Born-Infeld-like corrections to the Yang-Mills effective action will be studied. Non-anticommutative deformations of gauge and hyper-multiplet theories with extended super-symmetry induced by certain string backgrounds will be investigated, from the geometrical and quantum renormalizability points of view.
The search for evidence for integrable structures in N=4 SYM theory will be performed by calculating anomalous dimensions of twist-two higher spin operators at three and four loops. Background formalism for N=3 harmonic super-space formulation of N=4 SYM theory will be constructed and applied for the study of super-field correlation functions to further check AdS/CFT duality. Effective action in the hyper-multipelt sector of N=4 SYM theory and N=2 super-conformal models will be explored. The full dynamics of symmetric massless fields of all spins on the action level will be described to make it possible to analyse higher spin gauge theories at the quantum level; super-geometry of higher-spin extensions of super-gravity in tensorial super-spaces and its relationships with the twistor and harmonic approaches will be revealed. New models of quantum mechanics with extended super-symmetry will be constructed and applied to analyse AdS/CFT correspondence, exhibit integrable structures in super-symmetric gauge theories, explore (super) extensions of the Hall effect and study partial breaking of super-symmetry in super-particle models. The tools for achieving these objectives include the harmonic super-space, non-linear realization and twistor techniques, hamiltonian methods,Moyal-Weyl star product, super-embedding approach, geometrical methods of super-space super-gravity, background field method in (super)gauge theories, the pure spinor formalism of the covariant quantization of superstring. Many of these methods were proposed and worked out by the participants of the given Project.
As the general result of this investigation a new understanding of string/M-theory and brane dynamics will be achieved. The members of the consortium are world experts in their fields, so the research within the project should have a valuable outcome for the theory of fundamental interactions. Due to a combination of different approaches and methods, the results to be obtained will certainly have important applications in different research fields, including the neighbouring areas of theoretical and mathematical and high-energy physics.
SW7 2BZ London
Dubna, Moscow Region