Type II Superstring Field Theory: Geometric Approach and Operadic Description

TL;DR

This paper develops a geometric and algebraic framework for type II superstring field theory using the small Hilbert space, introducing an operadic interpretation and generalizing algebraic structures from bosonic strings.

Contribution

It constructs a novel geometric and algebraic formulation of type II superstring field theory, extending the BV master equation and operadic structures to the superstring context.

Findings

Defines elementary vertices via a minimal area problem.

Establishes an infinite tower of superstring field products.

Provides an operadic interpretation of the superstring field theory.

Abstract

We outline the construction of type II superstring field theory leading to a geometric and algebraic BV master equation, analogous to Zwiebach's construction for the bosonic string. The construction uses the small Hilbert space. Elementary vertices of the non-polynomial action are described with the help of a properly formulated minimal area problem. They give rise to an infinite tower of superstring field products defining a $\mathcal{N}=1$ generalization of a loop homotopy Lie algebra, the genus zero part generalizing a homotopy Lie algebra. Finally, we give an operadic interpretation of the construction.