Bosonic closed string field theory is famously governed by a Lie n-algebra for $n = \infty$ whose $k$-ary bracket is given by the genus-0 (k+1)-point function in the BRST complex of the string.

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

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?

  • $\begingroup$ Why do you use both "$L_\infty$-algebra" and "Lie $n$-algebra for $n = \infty$", when the article you linked indicates that they are the same thing? Is there a subtle distinction I am missing? $\endgroup$ Oct 21 '11 at 16:00
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    $\begingroup$ There is indeed no distinction, and that's what I wanted to implicitly emphasize a little, with an eye towards the BLG "3-algebra" excitement ncatlab.org/nlab/show/BLG+model#3AlgebraStructure. $\endgroup$ Oct 22 '11 at 17:42
  • $\begingroup$ Superstring field theory actually works differently than this "straightforward" generalization of bosonic string field theory. $\endgroup$ Jan 30 '14 at 14:12
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    $\begingroup$ There is an answer at physicsoverflow.org/4978 $\endgroup$ Jul 11 '15 at 7:33

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