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

Understand

The IKKT matrix model is a promising candidate for a nonperturbative formulation of superstring theory, in which spacetime is conjectured to emerge dynamically from the microscopic matrix degrees of freedom in the large-$N$ limit.

• Indeed in the Lorentzian version, Monte Carlo studies suggested the emergence of (3+1)-dimensional expanding space-time.
• Here we study the Euclidean version instead, and investigate an alternative scenario for dynamical compactification of extra dimensions via the spontaneous symmetry breaking (SSB) of 10D rotational symmetry.
• We perform numerical simulations based on the complex Langevin method (CLM) in order to avoid a severe sign problem.