Aspects non perturbatifs de la théorie des supercordes

Boris Pioline
Abstract : Superstring theories are to date the only viable candidate for quantum unification of gauge interactions with gravity. Until recently, these theories were only defined in the {\it weak coupling} regime by their perturbative series. Thanks to the recent discovery of duality symmetries, extending the electric-magnetic duality of Maxwell equations, these theories can now be identified as distinct approximations to a fundamental theory known as {\it M-theory}. Duality symmetries give access to {\it non-perturbative} effects in one string theory from {\it perturbative} computations in a dual theory. The first chapter of this thesis gives a non-technical introduction to these developments. 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 {\it exact} non-perturbative results for various couplings in the low energy effective action, and interpret the corresponding non-perturbative effects in terms of {\it instantonic configurations of $p$-branes} wrapped on supersymmetric cycles of the compactification manifold. Finally, we discuss a recent 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. Original publications for these results are included in the Appendices.
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Theses
Mathematical Physics. Université Pierre et Marie Curie - Paris VI, 1998. French


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Submitted on : Wednesday, February 20, 2002 - 11:14:51 PM
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Boris Pioline. Aspects non perturbatifs de la théorie des supercordes. Mathematical Physics. Université Pierre et Marie Curie - Paris VI, 1998. French. <tel-00001118>

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