D-instantons and Dualities in String Theory
In this thesis we study non-perturbative aspects of string theory. We focus our analysis on D-instanton effects which play key roles in the context of dualities, moduli stabilization and phenomenology. By translating ideas from instanton calculus in ordinary field theory, we develop tools to construct D-instanton moduli spaces which not only reproduce known field theory results, but also include novel “stringy” features. We apply these tools to supersymmetric gauge theories realized as world volume theories of spacefilling D-branes in non-trivial backgrounds. A key role is played by certain fermionic zero modes of the D-instantons. We show that, for configurations in which these zero modes are either lifted or projected out, new couplings appear in the effective action, even though their origin does not admit an obvious interpretation in terms of ordinary field theory. Such couplings are of great relevance for semi-realistic MSSM/GUT models since they may correspond to Yukawa couplings, Majorana mass terms for right-handed neutrinos or Polonyi terms, relevant for supersymmetry breaking.
In the last part of the thesis, we make use of various string theory dualities to compute multi-instanton corrections which are otherwise technically difficult to obtain from explicit D-instanton calculations. We compute one-loop diagrams with BPS particles in type IIA string theory configurations, involving spacefilling D-branes and orientifolds, and obtain exact quantum corrected gauge couplings in the dual type IIB picture. These quantum corrections involve infinite series of non- perturbative contributions from D-instantons. By lifting the one-loop calculation to the M-theory picture, we obtain a geometric understanding of the non-perturbative sector of a wide range of gauge theories and elucidate the underlying symmetries of the effective action.