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… (More)
In these notes we give an introduction to some of the concepts involved in constructing SM-like gauge theories in systems of branes at singularities of CY manifolds. These notes are an expanded version of lectures given by Herman Verlinde at the Cargese 2006 Summer School.
We give a concise geometric recipe for constructing D-brane gauge theories that exhibit metastable SUSY breaking. We present two simple examples in terms of branes at deformed CY singularities.
An analytic construction of compact Calabi-Yau manifolds with del Pezzo singularities is found. We present complete intersection CY manifolds for all del Pezzo singularities and study the complex deformations of these singularities. An example of the quintic CY manifold with del Pezzo 6 singularity and some number of conifold singularities is studied in… (More)
Recently, efforts to increase the toolkit which Escherichia coli cells possess for recombinant protein production in industrial applications, has led to steady progress towards making glycosylated therapeutic proteins. Although the desire to make therapeutically relevant complex proteins with elaborate human-type glycans is a major goal, the relatively poor… (More)
Connes and Kreimer have discovered the Hopf algebra structure behind the renor-malization of Feynman integrals. We generalize the Hopf algebra to the case of ribbon graphs, i.e. to the case of theories with matrix fields. The Hopf algebra is naturally defined in terms of surfaces corresponding to ribbon graphs. As an example, we discuss the renormalization… (More)
We find the leading RG logs in ϕ 4 theory for any Feynman diagram with 4 external edges. We obtain the result in two ways. The first way is to calculate the relevant terms in Feynman integrals. The second way is to use the RG invariance based on the Lie algebra of graphs introduced by Connes and Kreimer. The non-RG logs, such as (ln s/t) n , are discussed.