We analyze boundary states in the SU(2)k WZW model using open string field
theory in the level truncation approximation. We develop algorithms that allow
effective calculation of action in this model and we search for classical
solutions of the equations of motion, which are conjectured to describe
boundary states. We find three types of solutions. First, there are real
solutions that represent maximally symmetric Cardy boundary states and we show
that they satisfy certain selection rules regarding their SU(2) parameters.
Next, we find complex solutions that go beyond the SU(2) model and describe
maximally symmetric SL(2,C) boundary conditions. Finally, we find
exotic solutions that correspond to symmetry-breaking boundary states. Most of
real exotic solutions describe the so-called B-brane boundary states, but some
may represent yet unknown boundary states.Comment: v2: 95 pages, 6 figures, improved analysis of some solution