Closed string theory without level-matching at the free level

TL;DR

This paper explores a formulation of closed string field theory that removes the traditional level-matching constraint, enabling the study of new backgrounds and fluxes through an unconstrained free theory analysis.

Contribution

It provides a comprehensive analysis of the free theory without level-matching at the tachyonic and massless levels, paving the way for background studies without this constraint.

Findings

Unconstrained free theory at tachyonic and massless levels analyzed.

Potential for new backgrounds with fluxes due to trivial gauge fields.

Lays groundwork for studying string backgrounds without level-matching.

Abstract

In its traditional form, the string field in closed string field theory is constrained by the level-matching condition, which is imposed beside the action. By analogy with the similar problem for the Ramond sector, it was understood by Okawa and Sakaguchi how to lift this condition and work with unconstrained field by introducing spurious free fields. These authors also pointed out that new backgrounds may exist thanks to a new gauge field which is trivial on flat space, but can generate fluxes on a toroidal background. In this paper, we perform a complete study of the free theory at the tachyonic and massless levels with the aim of setting the stage for studying backgrounds without level-matching.