  The Lorentzian type IIB matrix model is a promising candidate for a
nonperturbative formulation of superstring theory. Recently we performed
complex Langevin simulations by adding a Lorentz invariant mass term as an IR
regulator and found a (1+1)-dimensional expanding spacetime with a Lorentzian
signature emerging dynamically at late times when the fermionic contribution is
omitted. Here we find that this is merely an artifact of the Lorentz boosts by
showing that the spontaneous breaking of rotational symmetry is eliminated if
one chooses a Lorentz frame appropriately. On the other hand, when we include
the fermionic contribution, we find some evidence suggesting the emergence of a
smooth (3+1)-dimensional expanding Lorentzian spacetime.
