"Complex Langevin analysis of the spontaneous rotational symmetry breaking in the dimensionally-reduced super-Yang-Mills models"

It has been speculated that the spontaneous symmetry breakdown (SSB) of the SO(D) rotational symmetry occurs in the matrix models obtained by the dimensional reduction of the super Yang-Mills (SYM)theory in D=6,10 dimensions, with the indices contracted by the Euclidean metric. The D=10 case corresponds to the IIB matrix model, which has been proposed as a nonperturbative definition of superstring theory, and the SSB of SO(D) corresponds to the dynamical generation of the spacetime in our universe. In the D=6,10 cases, Monte Carlo calculations suffer from a severe complex action problem due to the complex phase of the fermionic partition function. In this work, we apply the Complex Langevin Method (CLM) to these matrix 
models in order to study the SSB of the SO(D).