Probability distribution over some phenomenological models in the matrix model compactified on a torus

Abstract

We study some phenomenological models in a matrix model corresponding to the IIB matrix model compactified on a six-dimensional torus with magnetic fluxes. Extending our previous works, we examine a wider class of models: a Pati-Salam-like model with a gauge group U(4)*U_L(2)*U_R(2), and models where the gauge group U(4) is broken down to U_c(3)*U(1) and/or U_R(2) is broken down to U(1)^2. We find all the matrix configurations that yield matter content of all the phenomenological models whose gauge group is a subgroup of U(8). We then estimate semiclassically a probability distribution for the appearance of the phenomenological models.