The Statistics of Supersymmetric D-brane Models

TL;DR

This paper analyzes the statistical distribution of gauge groups and chiral matter in intersecting D-brane models within string theory, revealing correlations and effects of fluxes on these distributions.

Contribution

It generalizes number-theoretic methods to compute the asymptotic distributions of solutions to tadpole conditions in D-brane models, including correlations between gauge group rank and chiral generations.

Findings

Distribution of gauge group ranks and chiral generations computed

Found correlation between gauge group rank and number of chiral generations

Studied effects of fluxes on gauge theoretic distributions

Abstract

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 x 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.