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)×UL(2)×UR(2), and models where the gauge group U(4) is broken down to Uc(3)×U(1) and/or UR(2) is broken down to |${\mathrm {U}}(1)^2$|⁠. 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.