Number Of Chiral Generations Research Articles

The statistics of supersymmetric D-brane models

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 2 and T 6 / Z 2 × 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.

On the number of chiral generations in Z2× Z2 orbifolds

The data from collider experiments and cosmic observatories indicates the existence of three light matter generations. In some classes of string compactifications the number of generations is related to a topological quantity, the Euler characteristic. However, these do not explain the existence of three generations. In a class of free fermionic string models, related to the Z 2× Z 2 orbifold compactification, the existence of three generations is correlated with the existence of three twisted sectors in this class of compactifications. However, the three generation models are constructed in the free fermionic formulation and their geometrical correspondence is not readily available. In this paper we classify quotients of the Z 2× Z 2 orbifold by additional symmetric shifts on the three complex tori. We show that three generation vacua are not obtained in this manner, indicating that the geometrical structures underlying the free fermionic models are more esoteric.

Gauge Enhancement and Chirality Changes in Nonperturbative Orbifold Models

Consistent heterotic orbifold vacua, includingnonperturbative information, can be constructed.Generically, the usual modular invariance constraintsare violated and thus, anomalies are expected. However, five-branes do appear in the correct proportionjust to ensure the consistency of the full theory. Wefirst exemplify the situation in six dimensions, N = 1,where strong-coupling effects, implying the presence of five-branes, are better known.Explicit N = 1 models in D = 4, essentially inheritedfrom six dimensions, are then presented. In particularwe show concrete examples of models which exhibit nonperturbative transitions leading to gaugeenhancement and/or to a change in the number of chiralgenerations.

ORBIFOLD COMPACTIFICATIONS OF D<10 DIMENSIONAL FERMIONIC HETEROTIC STRING

Starting with D<10 dimensional fermionic heterotic string models and compactifying the remaining D−4 dimensions on Z3 orbifold, we study a scheme to combine the spin structure construction and the orbifold construction. It is shown that the scheme provides us with models which can easily accomodate a small number of chiral generations.