Aspects non perturbatifs de la theorie des supercordes

Abstract

This work is devoted to a study of some of the non-perturbative aspects of superstring theory that have come within reach thanks to dualities. The first chapter gives a non-technical zero-equation introduction to these developments intended for readers with a knowledge of quantum field theory (and french). The second chapter introduces the non-perturbative dualities that have been observed in gauge and supergravity theories as well as the non-perturbative BPS spectrum, and presents a novel duality relating the Higgs branches of certain supersymmetric N=2 gauge theories. In the third chapter, we briefly introduce the perturbative string theories and give some checks on the duality between four-dimensional N=4 string theories. From duality arguments, we obtain exact non-perturbative results for various couplings in the low energy effective action, and interpret the corresponding non-perturbative effects in terms of instantonic configurations of p-branes wrapped on supersymmetric cycles of the compactification manifold. Finally, we discuss the M(atrix) theory proposal of definition of M-theory in terms of large N supersymmetric U(N) gauge theories; we extend it to toroidal compactifications in constant background fields, and interpret the resulting spectrum of BPS states in terms of excitations in the gauge theory.