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The IKKT matrix model is a promising candidate for a nonperturbativeformulation of superstring theory, in which spacetime is conjectured to emergedynamically from the microscopic matrix degrees of freedom in the large-$N$limit. Indeed in the Lorentzian version, Monte Carlo studies suggested theemergence of (3+1)-dimensional expanding space-time. Here we study theEuclidean version instead, and investigate an alternative scenario fordynamical compactification of extra dimensions via the spontaneous symmetrybreaking (SSB) of 10D rotational symmetry. We perform numerical simulationsbased on the complex Langevin method (CLM) in order to avoid a severe signproblem. Furthermore, in order to avoid the singular-drift problem in the CLM,we deform the model and determine the SSB pattern as we vary the deformationparameter. From these results, we conclude that the original model has an SO(3)symmetric vacuum, which is consistent with previous results obtained by theGaussian expansion method (GEM). We also apply the GEM to the deformed matrixmodel and find consistency with the results obtained by the CLM.

Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model