Toward Realistic Intersecting D-Brane Models

We provide a pedagogical introduction to a recently studied class of phenomenologically interesting string models, known as Intersecting D-Brane Models. The gauge fields of the Standard-Model are localized on D-branes wrapping certain compact cycles on an underlying geometry, whose intersections can give rise to chiral fermions. We address the basic issues and also provide an overview of the recent activity in this field. This article is intended to serve non-experts with explanations of the fundamental aspects, and also to provide some orientation for both experts and non-experts in this active field of string phenomenology.Comment: 85 pages, 8 figures, Latex, Bibtex, v2: refs added, typos correcte

An Abundance of Heterotic Vacua

We explicitly construct the largest dataset to date of heterotic vacua arising from stable vector bundles on Calabi-Yau threefolds. Focusing on elliptically fibered Calabi-Yau manifolds with spectral cover bundles, we show that the number of heterotic models with non-zero number of generations is finite. We classify these models according to the complex base of their Calabi-Yau threefold and to the unification gauge group that they preserve in four dimensions. This database of the order of $10^7$ models, which includes potential Standard Model candidates, is subjected to some preliminary statistical analyses. The additional constraint that there should be three net generations of particles gives a dramatic reduction of the number of vacua.Comment: 27 pages, 12 figures, added reference

New Grand Unified Models with Intersecting D6-branes, Neutrino Masses, and Flipped SU(5)

We construct new supersymmetric SU(5) Grand Unified Models based on Z4 x Z2 orientifolds with intersecting D6-branes. Unlike constructions based on Z2 x Z2 orientifolds, the orbifold images of the three-cycles wrapped by D6-branes correspond to new configurations and thus allow for models in which, in addition to the chiral sector in 10 and 5-bar representations of SU(5), only, there can be new sectors with (15 + 15-bar) and (10 + 10-bar) vector-pairs. We construct an example of such a globally consistent, supersymmetric model with four-families, two Standard Model Higgs pair-candidates and the gauge symmetry U(5) x U(1) x Sp(4). In a N = 2 sector, there are 5 x (15 + 15-bar) and 1 x (10 + 10-bar) vector pairs, while another N = 1 sector contains one vector-pair of 15-plets. The N = 2 vector pairs can obtain a large mass dynamically by parallel D6-brane splitting in a particu- lar two-torus. The 15-vector-pairs provide, after symmetry breaking to the Standard Model (via parallel D-brane splitting), triplet pair candidates which can in principle play a role in generating Majorana- type masses for left-handed neutrinos, though the necessary Yukawa couplings are absent in the specific construction. Similarly, the 10- vector-pairs can play the role of Higgs fields of the flipped SU(5), though again there are phenomenological difficulties for the specific construction.Comment: 38 pages, 2 figures Minor corrections, references adde

Model building by coset space dimensional reduction in ten-dimensions with direct product gauge symmetry

We investigate ten-dimensional gauge theories whose extra six-dimensional space is a compact coset space, $S/R$, and gauge group is a direct product of two Lie groups. We list up candidates of the gauge group and embeddings of $R$ into them. After dimensional reduction of the coset space,we find fermion and scalar representations of $G_{\mathrm{GUT}} \times U(1)$ with $G_{\mathrm{GUT}}=SU(5), SO(10)$ and $E_6$ which accomodate all of the standard model particles. We also discuss possibilities to generate distinct Yukawa couplings among the generations using representations with a different dimension for $G_{\mathrm{GUT}}=SO(10)$ and $E_6$ models.Comment: 14 pages; added local report number, added refferenc

The Algebra of Grand Unified Theories

The Standard Model of particle physics may seem complicated and arbitrary, but it has hidden patterns that are revealed by the relationship between three "grand unified theories": theories that unify forces and particles by extending the Standard Model symmetry group U(1) x SU(2) x SU(3) to a larger group. These three theories are Georgi and Glashow's SU(5) theory, Georgi's theory based on the group Spin(10), and the Pati-Salam model based on the group SU(2) x SU(2) x SU(4). In this expository account for mathematicians, we explain only the portion of these theories that involves finite-dimensional group representations. This allows us to reduce the prerequisites to a bare minimum while still giving a taste of the profound puzzles that physicists are struggling to solve.Comment: 73 pages, 20 ps figure