Martijn Wijnholt

Building the standard model on a D3-brane

We motivate and apply a bottom-up approach to string phenomenology, which aims to construct the Standard Model as a decoupled world-volume theory on a D3-brane. As a concrete proposal for such a construction, we consider a single probe D3-brane on a partial resolution of a del Pezzo 8 singularity. The resulting world-volume theory reproduces the field content and interactions of the MSSM, however with a somewhat extended Higgs sector. An attractive feature of our approach is that the gauge and Yukawa couplings are dual to non-dynamical closed string modes, and are therefore tunable parameters.

D-branes at singularities, compactification, and hypercharge

We report on progress towards the construction of SM-like gauge theories on the world-volume of D-branes at a Calabi-Yau singularity. In particular, we work out the topological conditions on the embedding of the singularity inside a compact CY threefold, that select hypercharge as the only light U(1) gauge factor. We apply this insight to the proposed open string realization of the SM of hep-th/0508089, based on a D3-brane at a dP8 singularity, and present a geometric construction of a compact Calabi-Yau threefold with all the required topological properties.

A Higher Form (of) Mediation

We exhibit a simple and robust mechanism for bulk mediation of supersym- metry breaking between hidden and visible sectors localized on geometrically separated D-branes in type II string theory. The mediation proceeds via RR p-forms that couple via linear Chern-Simons terms to the abelian vector bosons on the branes. From a 4-d low energy perspective, the mechanism reduces to U(1) mediation.

Gluing branes — I

A bstractWe consider several aspects of holomorphic brane configurations. We recently showed that an important part of the defining data of such a configuration is the gluing morphism, which specifies how the constituents of a configuration are glued together, but is usually assumed to be vanishing. Here we explain the rules for computing spectra and interactions for configurations with non-vanishing gluing VEVs. We further give a detailed discussion of the D-terms for Higgs bundles, spectral covers and ALE fibrations. We highlight a stability criterion that applies to degenerate configurations of the spectral data, and address an apparent discrepancy between the field theory and ALE descriptions. This allows us to show that one gets walls of marginal stability in F -theory even though they are absent in the 11d supergravity description. We also propose a numerical approach for approximating the hermitian-Einstein metric of the Higgs bundle using balanced metrics.

Gluing Branes II: Flavour Physics and String Duality

A bstractRecently we discussed new aspects of degenerate brane configurations, which can appear in the context of heterotic strings, perturbative type II, or M/F-theory. Here we continue our study of degenerate brane configurations, focussing on two applications. First we show how the notion of gluing can be viewed as a tool to engineer flavour structures in F-theory and type IIb, such as models with bulk matter and with Yukawa textures arising from the holomorphic zero mechanism. We find that there is in principle enough structure to solve some of the major flavour problems without generating exotics. In particular, we show how this addresses the μ-problem, doublet/triplet splitting and proton decay. Secondly, we describe the Fourier-Mukai transform of heterotic monad constructions, which occur in the large volume limit of heterotic linear sigma model vacua. Degenerate structures again often appear. One may use this to explore strong coupling phenomena using heterotic/F-theory duality.

Cascading to the MSSM

The MSSM can arise as an orientifold of a pyramid-like quiver in the context of intersecting D-branes. Here we consider quiver realizations of the MSSM which can emerge at the bottom of a duality cascade. We classify all possible minimal ways this can be done by allowing only one extra node. It turns out that this requires extending the geometry of the pyramid to an octahedron. The MSSM at the bottom of the cascade arises in one of two possible ways, with the extra node disappearing either via Higgsing or confinement. Remarkably, the quiver of the Higgsing scenario turns out to be nothing but the quiver version of the left-right symmetric extension of the MSSM. In the minimal confining sce- nario the duality cascade can proceed if and only if there is exactly one up/down Higgs pair. Moreover, the symmetries of the octahedron naturally admit an automorphism of the quiver which solves a version of theproblem precisely when there are an odd number of generations.

Inside an enhançon: monopoles and dual Yang–Mills theory

Abstract In this paper we study wrapped brane configurations that give rise to three-dimensional pure Yang–Mills theory with eight supercharges. The corresponding supergravity solution is singular and it was conjectured that the singularity is removed by an enhancon mechanism. Instead, we incorporate non-perturbative gauge fields into supergravity and find a smooth solution for these configurations. Along the way we derive a non-Abelian supergravity Lagrangian for type IIA on K3 and explicit formulae for the toroidal reduction of the heterotic string with non-Abelian gauge fields. We proceed to analyze the duality with Yang–Mills theory and find that the dual background is a monopole configuration in little string theory.

Hitchin’s equations and M-theory phenomenology

Abstract Phenomenological compactifications of M -theory involve seven-manifolds with G 2 holonomy and various singularities. Here we study local geometries with such singularities, by thinking of them as compactifications of 7 d supersymmetric Yang–Mills theory on a three-manifold Q 3 . We give a general discussion of compactifications of 7 d Yang–Mills theory in terms of Higgs bundles on Q 3 . We show that they can be constructed using spectral covers, which are Lagrangian branes with a flat connection in the cotangent bundle T ∗ Q 3 . We explain the dictionary with ALE fibrations over Q 3 and conjecture that these configurations have G 2 holonomy. We further develop tools to study the low energy effective theory of such a model. We show that the naive massless spectrum is corrected by instanton effects. Taking the instanton effects into account, we find that the massless spectrum and many of the interactions can be computed with Morse theoretic methods.