IIB matrix model, bosonic master field, and emergent spacetime

TL;DR

This paper explores how the bosonic master field in the IIB matrix model can give rise to emergent classical spacetimes, providing new solutions for the master-field equation relevant to nonperturbative string theory.

Contribution

It presents new solutions to the bosonic master-field equation for the (D,N)=(10,4) case, advancing understanding of emergent spacetime in the IIB matrix model.

Findings

Explicit solutions for the (10,4) bosonic master-field equation.

Identification of critical points of the effective bosonic action.

Potential implications for replacing the big bang singularity.

Abstract

The IIB matrix model has been suggested as a particular formulation of nonperturbative superstring theory (M-theory). It has now been realized that an emerging classical spacetime may reside in its large-$N$ master field. This bosonic master field can, in principle, give rise to Minkowski and Robertson-Walker spacetimes. The outstanding task is to solve the bosonic master-field equation, which is essentially an algebraic equation. In this article, we present new results for the $(D,\,N)=(10,\,4)$ bosonic master-field equation of the IIB matrix model, where $D$ is the number of bosonic matrices and $N$ the matrix size. We also give, in a self-contained appendix, explicit results for critical points of the effective bosonic action. The main physics application of the (dimensionless) IIB matrix model may be in providing a (conformal) phase that replaces the Friedmann big bang singularity.