Geometry of Particle Physics

Katz and Vafa showed how charged matter can arise geometrically by the deformation of ADE-type orbifold singularities in type IIa, M-theory, and F-theory compactifications. In this paper we use those same basic ingredients, used there to geometrically engineer specific matter representations, here to deform the compactification manifold itself in a way which naturally compliments many features of unified model building. We realize this idea explicitly by deforming a manifold ...

This paper summarizes several developments in string-derived (Minimal Supersymmetric) Standard Models. Part one reviews the first string model containing solely the three generations of the Minimal Supersymmetric Standard Model and a single pair of Higgs as the matter in the observable sector of the low energy effective field theory. This model was constructed by Cleaver, Faraggi, and Nanopoulos in the Z_2 x Z_2 free fermionic formulation of weak coupled heterotic strings. Pa...

We introduce new techniques based on brane tilings to investigate D3-branes probing orientifolds of toric Calabi-Yau singularities. With these new tools, one can write down many orientifold models and derive the resulting low-energy gauge theories living on the D-branes. Using the set of ideas in this paper one recovers essentially all orientifolded theories known so far. Furthermore, new orientifolds of non-orbifold toric singularities are obtained. The possible applications...

Motivated by the simplicity and direct phenomenological applicability of field-theoretic orbifold constructions in the context of grand unification, we set out to survey the immensely rich group-theoretical possibilities open to this type of model building. In particular, we show how every maximal-rank, regular subgroup of a simple Lie group can be obtained by orbifolding and determine under which conditions rank reduction is possible. We investigate how standard model matter...

This brief survey aims to set the stage and summarize some of the ideas under discussion at the Workshop on Singular Geometry and Higgs Bundles in String Theory, to be held at the American Institute of Mathematics from October 30th to November 3rd, 2017. One of the most interesting aspects of the duality revolution in string theory is the understanding that gauge fields and matter representations can be described by intersection of branes. Since gauge theory is at the heart o...

We report the construction of large new classes of models which break supersymmetry dynamically. We then turn to model building. Two of the principal obstacles to constructing simple models of dynamical supersymmetry breaking are the appearance of Fayet-Iliopoulos D terms and difficulties in generating a $\mu$ term for the Higgs fields. Among the new models are examples in which symmetries prevent the appearance of Fayet-Iliopoulos terms. A gauge singlet field, that may play ...

After reviewing the general structure of supersymmetric intersecting brane world models, we discuss the issue of stringy gauge coupling unification for a natural class of MSSM-like models.

We propose a bottom-up approach to the building of particle physics models from string theory. Our building blocks are Type II D-branes which we combine appropriately to reproduce desirable features of a particle theory model: 1) Chirality ; 2) Standard Model group ; 3) N=1 or N=0 supersymmetry ; 4) Three quark-lepton generations. We start such a program by studying configurations of D=10, Type IIB D3-branes located at singularities. We study in detail the case of Z_N, N=1,0 ...

Brane systems provide a large class of gauge theories that arise in string theory. This paper demonstrates how such brane systems fit with a somewhat exotic geometric object, called the affine Grassmannian. This gives a strong motivation to study physical aspects of the affine Grassmannian. Explicit quivers are presented throughout the paper, and a quiver addition algorithm to generate the affine Grassmannian is introduced. An important outcome of this study is a set of quive...

We show that attempts to construct the standard model, or the MSSM, by placing D3-branes and D7-branes at a Z_N orbifold or orientifold singularity all require that the electroweak Higgs content is non-minimal. For the orbifold the lower bound on the number n(H) + n({\bar{H}}) of electroweak Higgs doublets is the number n(q^c_L)=6 of quark singlets, and for the orientifold the lower bound can be one less. As a consequence there is a generic flavour changing neutral current pr...