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: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
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.
Parent problems
- Special case of Background-independent definition of M-theory · open · from revision 1
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