$A_{\infty}$ Action of Open $\mathcal{N}=2$ Superstring Field Theory

TL;DR

The paper develops an open $\,\mathcal{N}=2$ string field theory with a cyclic $A_{ abla}$-algebra structure by leveraging the BRST cohomology relative to the $U(1)$ anti-ghost zero mode. It introduces a two-stage picture-dressing flow on coderivations to construct all higher products recursively while preserving the small Hilbert space, thereby avoiding singularities associated with picture-changing operators. The resulting action reproduces the perturbative S-matrix, matching worldsheet amplitudes with appropriate insertions of $X^{+}$ and $X^{-}$, and justifies the NS-sector focus via spectral-flow symmetry. This algebraic framework clarifies the interaction structure of open $\,\mathcal{N}=2$ strings and sets the stage for possible Extensions to closed strings, loop corrections, and connections to WZW-like formulations and double-copy constructions.

Abstract

We formulate a string field theory for open $\mathcal{N}=2$ strings with an $A_{\infty}$ algebra structure. Starting from the BRST cohomology relative to the U(1) anti-ghost zero-mode, we generalize [arXiv:1312.2948] and constructed all interacting vertices recursively and without singularity. We also show that our string field theory reproduces the correct perturbative S-matrix.