arXiv:hep-th/0311273 v2 4 Dec 2003 arxQatmMcaisand Mechanics Quantum Matrix w-iesoa tigTheory String Two-dimensional evc ePyiu Th Physique de Service nNntiilBackgrounds Non-trivial in UNIVERSIT egiAlexandrov Sergei h Thesis PhD oiu .-Saclay – eorique ´ AI XI PARIS E ´ Abstract String theory is the most promising candidate for the theory unifying all interactions including gravity. It has an extremely difficult dynamics. Therefore, it is useful to study some its simplifications. One of them is non-critical string theory which can be defined in low dimensions. A particular interesting case is 2D string theory. On the one hand, it has a very rich structure and, on the other hand, it is solvable. plete solution of 2D string theory in the simplest linear dilaton background was obtained using its representation as Matrix Quantum Mechanics. This matrix model provides a very powerful technique and reveals the integrability hidden in the usual CFT formulation. This thesis extends the matrix model description of 2D string theory to non-trivial back- grounds. We show how perturbations changing the background are incorporated into Matrix Quantum Mechanics. The perturbations are integrable and governed by Toda Lattice hier- archy. This integrability is used to extract various information about the perturbed system: correlation functions, thermodynamical behaviour, structure of the target space. The results concerning these and some other issues, like non-perturbative effects in non-critical string theory, are presented in the thesis. Acknowledgements This work was done at the Service de Physique Th´eorique du centre d’´etudes de Saclay. I would like to thank the laboratory for the excellent conditions which allowed to plish my work. Also I am grateful to CEA for the financial support during these three years. Equally, my gratitude is directed to the Laboratoire de Physique Th´eorique de l’Ecole Nor- male Sup´erieure where I also had th
