We conjecture a geometric criterion for determining whether supersymmetry is spontaneously broken in certain string backgrounds. These backgrounds contain wrapped branes at Calabi-Yau singularites with obstructions to deformation of the complex structure. We motivate our conjecture with a particular example: the Y 2,1 quiver gauge theory corresponding to a cone over the first del Pezzo surface, dP 1 . This setup can be analyzed using ordinary supersymmetric field theory methods, where we find that gaugino condensation drives a deformation of the chiral ring which has no solutions. We expect this breaking to be a general feature of any theory of branes at a singularity with a smaller number of possible deformations than independent anomalyfree fractional branes.

This paper discusses the minimal quiver gauge theory embedding of the standard model that could arise from brane world type string theory constructions. It is based on the low energy effective field theory of D-branes in the perturbative regime. The model differs from the standard model by the addition of one extra massive gauge boson, and contains only one additional parameter to the standard model: the mass of this new particle. The coupling of this new particle to the standard model is uniquely determined by input from the standard model and consistency conditions of perturbative string theory. We also study some aspects of the phenomenology of this model and bounds on its possible observation at the Large Hadron Collider.PACS numbers: 11.25. Uv, 11.25.Wx, 14.70.Pw Keywords: D-branes, Z' gauge bosons String Theory has long had a goal of unifying the Standard Model of particle physics with gravity in a consistent way. The possibility of a huge number of vacua where, in principle, anything can happen, suggests that we will find where we are in this landscape of vacua by doing sufficiently many experiments to determine the shape of the extra dimensions. If string theory is to be verified experimentally, it is useful to ask whether the Large Hadron Collider experiment will be able to see stringy physics directly and how to differentiate such effects from other results. Here we are limited by our calculational abilities.For these purposes, the most interesting scenarios for accelerator experiments are those where the string theory is perturbative, and the string scale is relatively low (a few TeV). The vast majority of these models are based on D-branes. Thus, we will ask a more limited question: Do low string scale D-brane models have universal low energy predictions for physics beyond the Standard Model that one can use to decide whether or not we live on a D-brane?The answer to this question is yes, but most of the tests rely on simple group theory properties of the spectrum, or directly observing the string theory resonances in an experiment. We want to find a uniquely stringy prediction that does not follow just from low energy effective field theory with the required matter content.The most important observation towards this goal is that the gauge group on a stack of identical D-branes is never SU (N Therefore, at tree level, the coupling constant of the U (1) part of the group and the SU (N ) part of the U (N ) gauge group are related, as well as the particles' charge under the U (1) and SU (N ), respectively. This is not required in pure effective field theory and constitutes a prediction for particle physics beyond the standard model based on string theory ideas. Our purpose is to explore this idea in the simplest possible setup compatible within an abstract D-brane setup.We will show that the minimal model compatible with perturbative D-brane string dynamics that contains the standard model has only one extra particle beyond the standard model. It is a massive vector boson that extends the color gauge gr...

We will demonstrate how calculations in toric geometry can be used to compute quantum corrections to the relations in the chiral ring for certain gauge theories. We focus on the gauge theory of the del Pezzo 2, and derive the chiral ring relations and quantum deformations to the vacuum moduli space using Affleck-Dine-Seiberg superpotential arguments. Then we calculate the versal deformation to the corresponding toric geometry using a method due to Altmann, and show that the result is equivalent to the deformation calculated using gauge theory. In an appendix we will apply this technique to a few other examples. This is a new method for understanding the infrared dynamics of certain quiver gauge theories.

We undertake a phenomenological study of the extra neutral Z' boson in the Minimal Quiver Standard Model and discuss limits on the model's parameters from previous precision electroweak experiments, as well as detection prospects at the Large Hadron Collider at CERN. We find that masses lower than around 700 GeV are excluded by the Z-pole data from the CERN-LEP collider, and below 620 GeV by experimental data from di-electron events at the Fermilab-Tevatron collider. We also find that at a mass of 1 TeV the LHC cross section would show a small peak in the di-lepton and top pair channel. *

Email:We study superpotential perturbations of q deformed N = 4 Yang-Mills for q a root of unity. This is a special case whose geometry is associated to an orbifold with three lines of codimension two singularities meeting at the origin. We perform field theory perturbations that leave only co-dimension three singularities of conifold type in the geometry. We show that there are two "fractional brane" solutions of the F-term equations for each singularity in the deformed geometry, and that the number of complex deformations of that geometry also matches the number of singularities. This proves that for this case there are no local or non-local obstructions to deformation. We also show that the associated Dijkgraaf-Vafa matrix model has a solvable sector, and that the loop equations in this sector encode the full deformed geometry of the theory. Contents