Solutions of the bosonic master-field equation from a supersymmetric matrix model

Abstract: It has been argued that the bosonic large-$N$ master field of the IIB matrix model can give rise to an emergent classical spacetime. In a paper, we have obtained solutions of a simplified bosonic master-field equation from a related matrix model. In this simplified equation, the effects of dynamic fermions were removed. We now consider the full bosonic master-field equation from a related supersymmetric matrix model for dimensionality $D=3$ and matrix size $N=3$. In this last equation, the effects of dynamic fermions are included. With an explicit realization of the random constants entering this algebraic equation, we establish the existence of nontrivial solutions. The small matrix size, however, does not allow us to make a definitive statement as to the appearance of a diagonal/band-diagonal structure in the obtained matrices.