Complex Langevin for Complex Actions: IKKT Matrix Model

In this talk, we report on the results of complex Langevin
simulations of the IKKT matrix model. This model is conjectured to be
a nonperturbative formulation of superstring theory in ten dimensions.
The spontaneous breaking of the SO(10) symmetry in this model can capture
the dynamical compactification of extra dimensions in string theory.
The Pfaffian in this model is inherently complex and thus can make
Monte Carlo simulations unreliable. The complex Langevin method can
handle wild fluctuations in the Pfaffian phase and give reliable
results. Our preliminary simulation results point to dynamical symmetry
breaking in the IKKT model