Complex Langevin study of spontaneous symmetry breaking in IKKT matrix model

The IKKT matrix model, in the large-$N$ limit, is conjectured to be a non-perturbative definition of the ten-dimensional type IIB superstring theory. In this work, we investigate the possibility of spontaneous breaking of the ten-dimensional rotational symmetry in the Euclidean IKKT model. Since the effective action, after integrating out the fermions, is inherently complex, we use the complex Langevin dynamics to study the model. In order to evade the singular-drift problem in the model, we add supersymmetry preserving deformations and then take the vanishing limit of the deformations. Our analysis suggests that the phase of the Pfaffian indeed induces the spontaneous SO(10) symmetry breaking in the Euclidean IKKT model.