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The IKKT matrix model (or the type IIB matrix model) is known as a promisingcandidate for a nonperturbative formulation of superstring theory in tendimensions. As a most attractive feature, the model admits the emergence of(3+1)-dimensional space-time associated with the spontaneous breaking of the(9+1)-dimensional Lorentz symmetry. Numerical confirmation of such a phenomenonhas been attempted for more than two decades. Recently it has been found thatthe sign problem, the main obstacle in simulating this model, can be overcomeby the complex Langevin method. It has been shown that the Lorenzian version ofthe model is smoothly connected with the Euclidean version, in which the SO(10)symmetry is found to be spontaneously broken to SO(3). Here we propose to add aLorentz invariant "mass" term to the original model and discuss a scenario that(3+1)-dimensional expanding space-time with Lorentzian signature appears atlate times. Some numerical results supporting this scenario are presented.

Signature change of the emergent space-time in the IKKT matrix model