The Statistics of Supersymmetric D-brane Models

Details The Statistics of Supersymmetric D-brane Models The Statistics of Supersymmetric D-brane Models

2004-11-18

arxiv.org/abs/hep-th/0411173v3

Nucl.Phys.B713:83-135,2005

Physics

High Energy Physics

High Energy Physics - Theory

62 pages, 31 figures, harvmac; v3: sections 3.2. + 3.7. added, figs. 7,28,29 added, figs. 24,25,26 corrected, refs. added, typ

Scientific paper

10.1016/j.nuclphysb.2005.02.005

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.

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