On Nontrivial Solutions around a Marginal Solution in Cubic Superstring   Field Theory
  We construct tachyon vacuum and half-brane solutions, using an extension of KBc algebra, in the theory around a type of identity-based marginal solutions in modified cubic superstring field theory. With explicit computations, we find that their vacuum energies are the same as those of corresponding solutions around the original theory. It implies that the vacuum energy for the identity-based marginal solution vanishes although straightforward computation of it is subtle. We also evaluate the gauge invariant overlaps for those nontrivial solutions. The values for them are deformed according to the marginal solution in the same way as the case of bosonic string field theory. 
Shoko Inatomi, Isao Kishimoto, Tomohiko Takahashi
hep-th