Exactly solvable matrix models with spontaneous breakdown ofSO(D)symmetry

Abstract

In the type IIB matrix model, which was proposed as a nonperturbative formulation of type IIB superstring theory, it is possible that our four-dimensional space-time appears dynamically as a brane in ten dimensions. This in particular requires the spontaneous breakdown of SO(10) symmetry, which was conjectured to be caused by the phase of the fermion integral. We present a concrete example of exactly solvable matrix models in which this happens. The models consist of D bosonic Hermitian matrices coupled to chiral fermions, and the $\mathrm{SO}(D)$ symmetry is spontaneously broken precisely due to the phase of the fermion determinant.