  We apply the complex Langevin method (CLM) to overcome the sign problem in 4D
SU(2) gauge theory with a theta term extending our previous work on the 2D U(1)
case. The topology freezing problem can be solved by using open boundary
conditions in all spatial directions, and the criterion for justifying the CLM
is satisfied even for large $\theta$ as far as the lattice spacing is
sufficiently small. However, we find that the CP symmetry at $\theta=\pi$
remains to be broken explicitly even in the continuum and infinite-volume
limits due to the chosen boundary conditions. In particular, this prevents us
from investigating the interesting phase structures suggested by the 't Hooft
anomaly matching condition. We also try the so-called subvolume method, which
turns out to have a similar problem. We therefore discuss a new technique
within the CLM, which enables us to circumvent the topology freezing problem
without changing the boundary conditions.
