Homotopy Operators and Identity-Based Solutions in Cubic Superstring   Field Theory
  We construct a class of nilpotent operators using the BRST current and ghost fields in superstring theory. The operator can be realized in cubic superstring field theory as a kinetic operator in the background of an identity-based solution. For a particular type of the deformed BRST operators, we find a homotopy operator and discuss its relationship to the cohomology in a similar way to the bosonic case, which has been elaborated by the authors. 
Shoko Inatomi, Isao Kishimoto and Tomohiko Takahashi
hep-th