BCFT moduli space in level truncation

We propose a new non-perturbative method to search for marginal deformations in level truncated open string field theory. Instead of studying the flatness of the effective potential for the marginal field (which is not expected to give a one-to-one parametrization of the BCFT moduli space), we identify a new non-universal branch of the tachyon potential which, from known analytic examples, is expected to parametrize the marginal flow in a much larger region of the BCFT moduli space. By a level 18 computation in Siegel gauge, we find an increasingly flat effective potential in the non-universal sector, connected to the perturbative vacuum and we confirm that the coefficient of the marginal field (lambda_SFT) has a maximum compatible with the value where the solutions stop existing in the standard Sen-Zwiebach approach. At the maximal reachable level, the effective potential still deviates from flatness for large values of the tachyon, but the Ellwood invariants stay close to the correct BCFT values on the whole branch and the full periodic moduli space of the cosine deformation is covered.