Comments on superstring field theory and its vacuum solution

TL;DR

This paper demonstrates the classical equivalence of NS cubic superstring field theories regardless of certain choices, and analyzes Erler's solution, showing it represents a true vacuum with trivial cohomology and zero boundary state.

Contribution

It proves the classical equivalence of different formulations of superstring field theory and provides a detailed analysis of Erler's vacuum solution.

Findings

NS cubic superstring field theories are classically equivalent

Erler's solution has trivial cohomology in all sectors

The boundary state for Erler's solution is zero

Abstract

We prove that the NS cubic superstring field theories are classically equivalent, regardless of the choice of Y_{-2} in their definition, and illustrate it by an explicit evaluation of the action of Erler's solution. We then turn to examine this solution. First, we explain that its cohomology is trivial also in the Ramond sector. Then, we show that the boundary state corresponding to it is identically zero. We conclude that this solution is indeed a closed string vacuum solution despite the absence of a tachyon field on the BPS D-brane.