Pure Gauge Configurations and Solutions to Fermionic Superstring Field Theories Equations of Motion

TL;DR

This paper investigates solutions to fermionic superstring field theory equations of motion, highlighting the role of pure gauge configurations, their divergences, and how to regularize the perturbation expansion.

Contribution

It introduces a matrix formulation for NS fermionic SFT and analyzes the divergence issues in pure gauge solutions, proposing a method to cure these divergences.

Findings

Pure gauge configurations can diverge in the perturbation expansion.

Adding specific terms regularizes the solutions and satisfies the equations of motion.

Matrix formulation facilitates uniform treatment of GSO sectors.

Abstract

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 theories 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.