A first look at the bosonic master-field equation of the IIB matrix model

TL;DR

This paper investigates a simplified algebraic form of the bosonic master-field equation in the IIB matrix model at low dimensions and matrix size, demonstrating the existence of solutions and revealing structural properties.

Contribution

It introduces a simplified algebraic approach to the bosonic master-field equation and provides explicit solutions at low dimensions and matrix size.

Findings

Existence of solutions for the simplified algebraic equation.

Discovery of a band-diagonal structure in one of the solution matrices.

Establishment of a pseudorandom constant realization in the model.

Abstract

The bosonic large-$N$ master field of the IIB matrix model can, in principle, give rise to an emergent classical spacetime. The task is then to calculate this master field as a solution of the bosonic master-field equation. We consider a simplified version of the algebraic bosonic master-field equation and take dimensionality $D=2$ and matrix size $N=6$. For an explicit realization of the pseudorandom constants entering this simplified algebraic equation, we establish the existence of a solution and find, after diagonalization of one of the two obtained matrices, a band-diagonal structure of the other matrix.