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

TL;DR

This paper finds solutions to the full bosonic master-field equation in a supersymmetric matrix model with fermionic effects included, providing insights into emergent spacetime from matrix models.

Contribution

It extends previous work by solving the full bosonic master-field equation with fermionic effects in a supersymmetric matrix model at small matrix size.

Findings

Existence of nontrivial solutions established

Explicit realization of random constants used

Limited by small matrix size for structural analysis

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 recent 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.