The main goal of this project is to investigate certain aspects of noncommutative gauge field theories, M-theory, strings, superstrings, black holes and D-branes.

It is planned to study noncommutative gauge theories and associated reduced models. Using the methods of nonperturbative gauge theories, it is expected to investigate properties of the Wilson loops in noncommutative gauge theories, derive a path-integral representation of the Seiberg-Witten map between commutative and noncommutative gauge fields and to study classical solitonic solutions. The expected results will be applicable in D-brane physics, the problem of tachyonic condensation and ordinary Yang-Mills theory at large N.

The second related subject concerns the correspondence between superstring on anti-de-Sitter space and supersymmetric gauge theories at large N. It is planned to investigate the properties of the Wilson loops in supersymmetric large-N gauge theories and to verify whether they satisfy the loop equations. It is expected to investigate the consistency of the superstring ansatz for the Wilson loops with a supersymmetric analog of the loop equations for the case of 4 extended sypersymmetries. This may help to find a solution to these equations in the physically most interesting case of asymptotically free theories in which super-conformal symmetry is broken by quantum corrections and might shed light on the old problem of finding a string representation for the Wilson loop expectation values in gauge theories.

It is planned to study the thermodynamics of D-branes in superstring theory using the formulation of matrix theory at finite temperature, which is a non-perturbative formulation of superstring theory. It is intended to test the relation between D-branes at finite temperature and non-extremal black holes in string theory using a novel technique for studying the effective interactions of D0-branes in a thermal state recently formulated by the project participants. It is proposed to analyse the D-brane system with this effective interaction paying particular attention to the lowest energy bound state. This will give a new way of computing the entropy, size, mass and other properties of the thermal D-brane state which can then be compared with those known properties of a non-extremal black hole.

In order to develop the string theory in the non-critical d=2,3,4 dimensions, it is planned to investigate the three dimensional Ising model, which is a gauge theory with the simplest group Z_2. The model of so-called sign factor will be formulated as a fermionic string theory and will be investigated in connection with the ground state structure of gauge theories. Since the fermionic string can be considered as a chain of spins with the local, nearest-neighbor interactions, the spin-chain models with affine quantum group symmetries, the integrable models of strongly correlated electrons with impurities will be studied in order to develop the inhomogenouity in the chain as trivial string.

The main tasks of the investigation include:

- noncommutative gauge theories and matrix models,

- aspects of background independence,

- description of D-branes as noncommutative solitons,

- correspondence between superstring theory on anti-de-Sitter space and gauge theories at large N,

- Wilson loops in supersymmetric gauge theories and loop equations,

- thermodynamics of D-branes in superstring theory and Matrix theory,

- relation of D-branes and non-extremal black holes,

- srting representation 3D Ising and related models.

The investigations will use the methods of the Quantum Field Theory, General Relativity and Statistical Mechanics.