QFT In the literature: contested

Do four expanding spacetime dimensions emerge in the IKKT model

In plain words

A model built from ten large matrices is proposed as a complete definition of one string theory. Whether it produces a universe with three large expanding space directions is unknown.

Precise statement

The type IIB (IKKT) matrix model of ten $N$ x N Hermitian bosonic matrices and fermions is proposed as a nonperturbative definition of type IIB string theory. Determine whether its Lorentzian version at large N dynamically generates a smooth expanding $(3+1)$-dimensional spacetime with $\mathrm{SO}(9) \to \mathrm{SO}(3)$ breaking, rather than singular configurations.

What would settle it

Large-N simulations of the Lorentzian model with controlled sign-problem treatment showing (or excluding) smooth emergent 3+1 expansion.

Status in the literature

Unverified note

Early Lorentzian simulations (2012) reported three expanding directions; later work found singular Pauli-matrix-like structures tied to approximations, and complex Langevin studies continued through 2025.