### Math-Physics Joint Seminar

Wednesday, May 2, 2018 - 2:00pm

#### Kantaro Ohmori

IAS

Location

University of Pennsylvania

4C2

Note unusual date and time. Joint with the Deformation Seminar.

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.