On the classical equivalence of superstring field theories

TL;DR

This paper demonstrates the classical equivalence of cubic and non-polynomial open superstring field theories through explicit mappings that preserve solutions, gauge orbits, and physical spectra, extending to non-BPS and multi-D-brane systems.

Contribution

It constructs explicit mappings showing the classical equivalence of different superstring field theories and analyzes their solutions, including BPS and non-BPS cases.

Findings

Mappings preserve the action and gauge orbits between theories.

Analytical solutions form a one-parameter family with identical action and empty cohomology.

Open superstring field theory can describe vacuum solutions around BPS D-branes.

Abstract

We construct mappings that send solutions of the cubic and non-polynomial open superstring field theories to each other. We prove that the action is invariant under the maps and that gauge orbits are mapped into gauge orbits. It follows that the perturbative spectrum around solutions is the same in both theories. The mappings also preserve the string field reality condition. We generalize to the cases of a non-BPS D-brane and of multi-D-brane systems. We analyze the recently found analytical solutions of the cubic action, both in the BPS sector and the non-BPS sector and show that they span a one parameter family of solutions with empty cohomology and identical action, which suggests that they are gauge equivalent. We write the gauge transformations relating these solutions explicitly. This seems to suggest that open superstring field theory is able to describe a vacuum solution even around a BPS D-brane.