Consistent decompositions of moduli spaces of Riemann surfaces yield homotopy algebras such as A_\infinity or L_\infinity algebras, that essentially define string field theories (SFTs), supposed to be a non-perturbative definition of the string theory. In the case of open Riemann surfaces, the Strebel differential defines the associative product called Witten’s star-product.
In this talk I would like to describe an attempt to generalize this well-known construction to the case of super-Riemann surfaces and supermoduli of those.
Unlike the case of usual Riemann surfaces, there cannot be an associative product, hence one needs to introduce higher products to construct the desired A_\infty structure.
In this talk I only construct the 2-ary and 3-ary product, and higher products remain to be constructed.
The desired A_\infty structure is expected to be isomorphic to A_\infty structures found by others using other methods in the context of superstring field theory.