Sommaire:

Non-perturbative effects play an extremely important role in the modern theoretical physics. For example, they are known to be responsible for various physical phenomena such as confinement and dualities. An especially rich arena for these effects is provided by gauge and string theories. In particular, for theories with N=2 supersymmetry in 4 dimensions, recent years marked a remarkable progress in understanding their non-perturbative dynamics. May be one of the most intriguing findings is the appearance of integrability in several, sometimes differently looking problems. These results provide non-trivial relations between different physical systems and mathematical constructions and give a hope that many longstanding problems can be in fact exactly solvable. The thesis is supposed to explore these relations between non-perturbative effects and integrability. More precisely, it is suggested to study the problem of compactifications of string theories which preserve N=2 supersymmetry. Their low-energy effective action is completely determined by a metric on a certain moduli space which is known to receive instanton corrections. Although many of them have been already found, the complete non-perturbative description is still out of reach. On the other hand, its relevance goes much beyond the effective action mentioned above since it should encode information about S-duality, non-perturbative mirror symmetry, wall-crossing, supersymmetric black holes. Thus, working in this direction would allow not only to obtain interesting results, but also to study many related subjects in string theory, mathematics and other research areas.

Pour plus d'informations, merci de contacter Caron D.