Continuing our recent work hep-th/0411173, we study the statistics of fourdimensional, supersymmetric intersecting D-brane models in a toroidal orientifold background. We have performed a vast computer survey of solutions to the stringy consistency conditions and present their statistical implications with special emphasis on the frequency of Standard Model features. Among the topics we discuss are the implications of the K-theory constraints, statistical correlations among physical quantities and an investigation of the various statistical suppression factors arising once certain Standard Model features are required. We estimate the frequency of an MSSM like gauge group with three generations to be one in a billion.

We investigate the statistics of the phenomenologically important D-brane sector of string compactifications. In particular for the class of intersecting D-brane models, we generalise methods known from number theory to determine the asymptotic statistical distribution of solutions to the tadpole cancellation conditions. Our approach allows us to compute the statistical distribution of gauge theoretic observables like the rank of the gauge group, the number of chiral generations or the probability of an SU (N ) gauge factor. Concretely, we study the statistics of intersecting branes on T 2 and T 4 /Z Z 2 and T 6 /Z Z 2 × Z Z 2 orientifolds.Intriguingly, we find a statistical correlation between the rank of the gauge group and the number of chiral generations. Finally, we combine the statistics of the gauge theory sector with the statistics of the flux sector and study how distributions of gauge theoretic quantities are affected. 11/2004

Using previous results on the statistics of intersecting D6-brane models on T 6 /Z ′ 6 we analyse solutions that resemble the gauge group and matter content of the supersymmetric standard model. In particular the structure of the hidden sector, the gauge coupling constants and chiral exotic matter content are computed and classified for all possible standard model-like configurations on this background. It turns out that the number of chiral exotics, Higgses and values of gauge couplings are strongly correlated. Some examples with the chiral spectrum of the supersymmetric standard model plus vector-like states and a massless U(1) B−L are discussed in detail.fgmeiner@nikhef.nl Gabriele.Honecker@cern.ch

We perform a complete analysis of one-loop threshold corrections to the gauge couplings of fractional D6-branes. This includes besides SU(N) also symplectic, orthogonal and massless Abelian gauge factors and the full computation of contributions from discrete and continuous Wilson lines and brane displacements. Two classes of globally consistent supersymmetric compactifications with Standard Model spectra on T 6 /Z 6 and T 6 /Z ′ 6 are presented in detail with the latter exhibiting the potential of supersymmetry breaking via a hidden sector gaugino condensate. The T 6 /Z ′ 6 Standard Models are completely classified, and it turns out that out of 768 distinct D6-brane configurations only 16 different sets of massless spectra and ten distinct values of gauge couplings at one-loop arise. The gauge threshold corrections enhance the diversity to 196 nonequivalent models.

We provide a complete classification and statistical analysis of all type IIA orientifold compactifications with intersecting D6-branes on the orbifold T 6 /Z ′ 6 . The total number of four dimensional N=1 supersymmetric models is found to be O(10 23 ). After a statistical analysis of the gauge sector properties of all possible solutions, we study three subsets of configurations which contain the chiral matter sector of the standard model, a Pati-Salam or SU (5) GUT model, respectively. We find O(10 15 ) compactifications with an MSSM and O(10 11 ) models with a Pati-Salam sector. Along the way we derive an explicit algebraic formulation for the computation of the non-chiral matter spectrum for all Z N orbifolds. A. The non-chiral models in cycle language 36 B. Search for SO(2N ) or Sp(2N ) gauge groups 36 C. The lattice of three-cycles 37 D. Bulk wrapping numbers 37 D.1 Standard model example 38 D.2 Pati-Salam example 38 References 43 -1 -