We construct a new solution of the superstring equation of motion and show that this solution satisfies two of Sen's conjectures and does not require "phantom terms."Dedicated to the memory of P. B. Medvedev

In construction of analytical solutions to open string field theories pure gauge configurations parameterized by wedge states play an essential role. These pure gauge configurations are constructed as perturbation expansions and to guaranty that these configurations are asymptotical solutions to equations of motion one needs to study convergence of the perturbation expansions. We demonstrate that for the large parameter of the perturbation expansion these pure gauge truncated configurations give divergent contributions to the equation of motion on the subspace of the wedge states. We perform this demonstration numerically for the pure gauge configurations related to tachyon solutions for the bosonic and NS fermionic SFT. By the numerical calculations we also show that the perturbation expansions are cured by adding extra terms. These terms are nothing but the terms necessary to make valued the Sen conjectures. that is the same as the equation of motion for the open bosonic and cubic superstring SFTs (one has just removed the hats in the later cases). Φ is 2 × 2 matrix where the components are string fields belonging to the GSO(+) and GSO(−) sectors. Pure 1 We call the NS fermionic SFT the NS string field theory with two sectors, GSO(+) and GSO(−) and we call the superstring SFT (SSFT) the NS string field theory with the GSO(+) sector only.2 The physical meaning of this solution is still unclear for us. It may happen that it is related with a spontaneous supersymmetry breaking (compare with [38]).3 Let us remind that the NS fermionic SFT with two sectors is used to describe non-BPS branes. The Sen conjecture has been checked by level truncations for the non-polynomial and cubic cases in [46] and [40], respectively.

Recent results on solutions to the equation of motion of the cubic fermionic string field theory and an equivalence of non-polynomial and cubic string field theory are discussed. To have a possibility to deal with both GSO(+) and GSO(−) sectors in the uniform way a matrix formulation for the NS fermionic SFT is used. In constructions of analytical solutions to open string field theories truncated pure gauge configurations parameterized by wedge states play an essential role. The matrix form of this parametrization for the NS fermionic SFT is presented. Using the cubic open superstring field theory as an example we demonstrate explicitly that for the large parameter of the perturbation expansion these truncated pure gauge configurations give divergent contributions to the equation of motion on the subspace of the wedge states. The perturbation expansion is cured by adding extra terms that are nothing but the terms necessary for the equation of motion contracted with the solution itself to be satisfied.

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Simple analytic solution to cubic Neveu-Schwarz String Field Theory including the GSO(−) sector is presented. This solution is an analog of the Erler-Schnabl solution for bosonic case and one of the authors solution for the pure GSO(+) case. Gauge transformations of the new solution to others known solutions for the N S string tachyon condensation are constructed explicitly. This gauge equivalence manifestly supports the early observed fact that these solutions have the same value of the action density.