Timo Weigand

Spacetime instanton corrections in 4D string vacua: The Seesaw mechanism for D-Brane models

Abstract We systematically investigate instanton corrections from wrapped Euclidean D-branes to the matter field superpotential of various classes of N = 1 supersymmetric D-brane models in four dimensions. Both gauge invariance and the counting of fermionic zero modes provide strong constraints on the allowed non-perturbative superpotential couplings. We outline how the complete instanton computation boils down to the computation of open string disc diagrams for boundary changing operators multiplied by a one-loop vacuum diagram. For concreteness we focus on E2-instanton effects in type IIA vacua with intersecting D6-branes, however the same structure emerges for type IIB and heterotic vacua. The instantons wrapping rigid cycles can potentially destabilise the vacuum or generate perturbatively absent matter couplings such as proton decay operators, μ-parameter or right-handed neutrino Majorana mass terms. The latter allow the realisation of the seesaw mechanism for MSSM like intersecting D-brane models.

Lectures on F-theory compactifications and model building

These lecture notes are devoted to formal and phenomenological aspects of F-theory. We begin with a pedagogical introduction to the general concepts of F-theory, covering classic topics such as the connection to type IIB orientifolds, the geometry of elliptic fibrations and the emergence of gauge groups, matter and Yukawa couplings. As a suitable framework for the construction of compact F-theory vacua we describe a special class of Weierstrass models called Tate models, whose local properties are captured by the spectral cover construction. Armed with this technology we proceed with a survey of F-theory grand unified theory (GUT) models, aiming at an overview of basic conceptual and phenomenological aspects, in particular in connection with GUT breaking via hypercharge flux.

Global F-theory GUTs

We construct global F-theory GUT models on del Pezzo surfaces in compact Calabi–Yau fourfolds realized as complete intersections of two hypersurface constraints. The intersections of the GUT brane and the flavour branes as well as the gauge flux are described by the spectral cover construction. We consider a split S [ U ( 4 ) × U ( 1 ) X ] spectral cover, which allows for the phenomenologically relevant Yukawa couplings and GUT breaking to the MSSM via hypercharge flux while preventing dimension-4 proton decay. General expressions for the massless spectrum, consistency conditions and a new method for the computation of curvature-induced tadpoles are presented. We also provide a geometric toolkit for further model searches in the framework of toric geometry. Finally, an explicit global model with three chiral generations and all required Yukawa couplings is defined on a Calabi–Yau fourfold which is fibered over the del Pezzo transition of the Fano threefold P 4 [ 4 ] .

D-brane Instantons in Type II String Theory

We review recent progress in determining the effects of d-brane instantons in supersymmetric compactifications of Type II string theory to four dimensions. We describe the abstract d-brane instanton calculus for holomorphic couplings such as the superpotential, the gauge kinetic function, and higher fermionic F-terms, and we briefly discuss the implications of background fluxes for the instanton sector. We then summarize the concrete consequences of stringy d-brane instantons for the construction of semirealistic models of particle physics or supersymmetry breaking in compact and noncompact geometries.

On Abelian Gauge Symmetries and Proton Decay in Global F-theory GUTs

The existence of Abelian gauge symmetries in four-dimensional

One in a billion: MSSM-like D-brane statistics

F

Loop-corrected compactifications of the heterotic string with line bundles

-theory compactifications depends on the global geometry of the internal Calabi-Yau four-fold and has important phenomenological consequences. We study conceptual and phenomenological aspects of such

The statistics of supersymmetric D-brane models

U(1)

GUTs in type IIB orientifold compactifications

symmetries along the Coulomb and the Higgs branch. As one application we examine Abelian gauge factors arising after a certain global restriction of the Tate model that goes beyond a local spectral cover analysis. In

Nonperturbative yukawa couplings from string instantons.

SU(5)