Towards Weakly Constrained Double Field Theory

TL;DR

This paper develops a new effective field theory framework for string winding modes in double field theory that relaxes the strong constraint, using Radon transform techniques to maintain consistency.

Contribution

It introduces a novel formalism employing Radon transform to describe weakly constrained double fields without strong constraint, enabling a consistent gauge theory.

Findings

Constructed a gauge-invariant action without strong constraint.

Demonstrated the use of Radon transform for weakly constrained fields.

Linked the formalism to closed string field theory.

Abstract

We show that it is possible to construct a well-defined effective field theory incorporating string winding modes without using strong constraint in double field theory. We show that X-ray (Radon) transform on a torus is well-suited for describing weakly constrained double fields, and any weakly constrained fields are represented as a sum of strongly constrained fields. Using inverse X- ray transform we define a novel binary operation which is compatible with the level matching constraint. Based on this formalism, we construct a consistent gauge transform and gauge invariant action without using strong constraint. We then discuss the relation of our result to the closed string field theory. Our construction suggests that there exists an effective field theory description for massless sector of closed string field theory on a torus in an associative truncation.