Perturbative Double Field Theory on General Backgrounds

TL;DR

This paper develops a background covariant perturbation theory for double field theory, expanding the action to cubic order and confirming its applicability to arbitrary curved backgrounds like group manifolds, aligning with string theory results.

Contribution

It introduces a background covariant perturbation framework for double field theory and verifies its consistency with string theory on group manifolds.

Findings

Derived the cubic action in background covariant form.

Confirmed agreement with string field theory on group backgrounds.

Demonstrated applicability of double field theory to arbitrary curved solutions.

Abstract

We develop the perturbation theory of double field theory around arbitrary solutions of its field equations. The exact gauge transformations are written in a manifestly background covariant way and contain at most quadratic terms in the field fluctuations. We expand the generalized curvature scalar to cubic order in fluctuations and thereby determine the cubic action in a manifestly background covariant form. As a first application we specialize this theory to group manifold backgrounds, such as $SU(2) \simeq S^3$ with $H$-flux. In the full string theory this corresponds to a WZW background CFT. Starting from closed string field theory, the cubic action around such backgrounds has been computed before by Blumenhagen, Hassler and L\"ust. We establish precise agreement with the cubic action derived from double field theory. This result confirms that double field theory is applicable to arbitrary curved background solutions, disproving assertions in the literature to the contrary.