Superstring field theory equivalence: Ramond sector

TL;DR

This paper investigates the classical relationship between two superstring field theories, highlighting issues with gauge transformations in the Ramond sector and proposing a formal equivalence that hints at a possible consistent modification.

Contribution

It constructs mappings between the cubic and non-polynomial superstring theories, extending the classical equivalence to include the Ramond sector despite gauge transformation issues.

Findings

Classical solutions are mapped between theories, preserving gauge invariance.

The perturbative spectrum around solutions is isomorphic.

The equivalence is formal due to gauge symmetry issues.

Abstract

We prove that the finite gauge transformation of the Ramond sector of the modified cubic superstring field theory is ill-defined due to collisions of picture changing operators. Despite this problem we study to what extent could a bijective classical correspondence between this theory and the (presumably consistent) non-polynomial theory exist. We find that the classical equivalence between these two theories can almost be extended to the Ramond sector: We construct mappings between the string fields (NS and Ramond, including Chan-Paton factors and the various GSO sectors) of the two theories that send solutions to solutions in a way that respects the linearized gauge symmetries in both sides and keeps the action of the solutions invariant. The perturbative spectrum around equivalent solutions is also isomorphic. The problem with the cubic theory implies that the correspondence of the linearized gauge symmetries cannot be extended to a correspondence of the finite gauge symmetries. Hence, our equivalence is only formal, since it relates a consistent theory to an inconsistent one. Nonetheless, we believe that the fact that the equivalence formally works suggests that a consistent modification of the cubic theory exists. We construct a theory that can be considered as a first step towards a consistent RNS cubic theory.