# Open superstring field theory based on the supermoduli space

## TL;DR

This paper introduces a new formulation of open superstring field theory based on supermoduli space covering, explicitly constructing gauge-invariant actions up to quartic interactions that naturally realize an $A_$ structure.

## Contribution

It provides a novel approach to superstring field theory using supermoduli space covering, explicitly constructing gauge-invariant actions and $A_$ structures up to quartic order.

## Key findings

- Explicit construction of gauge-invariant action up to quartic interactions.
- Representation of interactions as integrals over supermoduli space regions.
- Natural realization of $A_$ structure in the theory.

## Abstract

We present a new approach to formulating open superstring field theory based on the covering of the supermoduli space of super-Riemann surfaces and explicitly construct a gauge-invariant action in the Neveu-Schwarz sector up to quartic interactions. The cubic interaction takes a form of an integral over an odd modulus of disks with three punctures and the associated ghost is inserted. The quartic interaction takes a form of an integral over one even modulus and two odd moduli, and it can be interpreted as the integral over the region of the supermoduli space of disks with four punctures which is not covered by Feynman diagrams with two cubic vertices and one propagator. As our approach is based on the covering of the supermoduli space, the resulting theory naturally realizes an $A_\infty$ structure, and the two-string product and the three-string product used in defining the cubic and quartic interactions are constructed to satisfy the $A_\infty$ relations to this order.