  In string or M theories, the spontaneous breaking of 10D or 11D Lorentz
symmetry is required to describe our space-time. A direct approach to this
issue is provided by the IIB matrix model. We study its 4D version, which
corresponds to the zero volume limit of 4D super SU(N) Yang-Mills theory. Based
on the moment of inertia as a criterion, spontaneous symmetry breaking (SSB)
seems to occur, so that only one extended direction remains, as first observed
by Bialas, Burda et al. However, using Wilson loops as probes of space-time we
do not observe any sign of SSB in Monte Carlo simulations where N is as large
as 48. This agrees with an earlier observation that the phase of the fermionic
integral, which is absent in the 4D model, should play a crucial role if SSB of
Lorentz symmetry really occurs in the 10D IIB matrix model.
