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Non-perturbative formulations are essential to understand the dynamicalcompactification of extra dimensions in superstring theories. The type IIB(IKKT) matrix model in the large-$N$ limit is one such conjectured formulationfor a ten-dimensional type IIB superstring. In this model, a smooth spacetimemanifold is expected to emerge from the eigenvalues of the ten bosonicmatrices. When this happens, the SO(10) symmetry in the Euclidean signaturemust be spontaneously broken. The Euclidean version has a severe sign problemsince the Pfaffian obtained after integrating out the fermions is inherentlycomplex. In recent years, the complex Langevin method (CLM) has successfullytackled the sign problem. We apply the CLM method to study the Euclideanversion of the type IIB matrix model and investigate the possibility ofspontaneous SO(10) symmetry breaking. In doing so, we encounter asingular-drift problem. To counter this, we introduce supersymmetry-preservingdeformations with a Myers term. We study the spontaneous symmetry breaking inthe original model at the vanishing deformation parameter limit. Our analysisindicates that the phase of the Pfaffian induces the spontaneous SO(10)symmetry breaking in the Euclidean type IIB model.

Investigating Spontaneous SO(10) Symmetry Breaking in Type IIB Matrix Model