Perturbative Double Field Theory on General Backgrounds

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 Lüst. 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.

36 pages, v2: minor clarifications

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• Background Independent Double Field Theory at Order ${\alpha }^{\prime }$: Metric vs. Frame-like Geometry
• Probing the String Winding Sector
• DFT in supermanifold formulation and group manifold as background geometry
• Supergravity with Doubled Spacetime Structure
• Geometric Low-Energy Effective Action in a Doubled Spacetime
• Double Field Theory on Group Manifolds in a Nutshell
• Gravitational Core of Double Field Theory: Lecture Notes
• Duality Covariant Solutions in Extended Field Theories