One might therefore expect that, analogously, closed superstring field theory (in any of its variants) is governed by a lift of that to a super Lie n-algebra for $n = \infty$.
The closest to an identification of such that I am aware of is in
- Yuji Okawa, Barton Zwiebach, Heterotic String Field Theory (arXiv:hep-th/0406212)
where substructures of the bosonic string field $L_\infty$-algebra are paired with the super-ingredients. This seems to go in the right direction, but does not quite identify a super $L_\infty$-algebra structure.
Is there, meanwhile, anything more known that may complete the picture here?