Tachyon potential in KBc subalgebra

We evaluate the classical action and the effective tachyon potential of open string field theory within KBc subalgebra, which is extensively used in analytic solution for tachyon condensation recently found by Erler and Schnabl. It is found that the level expansion of the string field terminates at level 3. We find that the closed string vacuum is a saddle point of the classical action. We also evaluate the effective potential for tachyon field. The closed string vaccum becomes stable by integrationg out an auxiliary field. It is found that the effective potential is bounded below hence has no runaway direction. We also argue validity of simple identity based solution.