Gauge theory of Kaluza-Klein and winding modes

TL;DR

This paper reformulates double field theory using a Kaluza-Klein inspired approach that maintains manifest O(d,d) invariance and describes the full spectrum of Kaluza-Klein and winding modes.

Contribution

It introduces a new formulation of double field theory that incorporates all Kaluza-Klein and winding modes without truncation, using a gauge structure related to the tensor hierarchy.

Findings

The theory is manifestly O(d,d) invariant.

It describes the full tower of Kaluza-Klein and winding modes.

The gauge algebra involves a Courant bracket and tensor hierarchy structures.

Abstract

We perform a Kaluza-Klein inspired rewriting of double field theory by splitting the coordinates into `compact' and `non-compact' directions. There is no truncation of the compact coordinates or their duals, and so this formulation is manifestly O(d,d) invariant, with d the number of compact directions. The action can serve as starting point for arbitrary Kaluza-Klein ansaetze. For a torus background the theory describes the full tower of Kaluza-Klein modes or, in the dual frame, of the winding modes. The Kaluza-Klein vector is a gauge field for the duality-covariantized Courant bracket algebra rather than a Lie algebra. Gauge covariance requires the inclusion of the 2-form gauge potential descending from the Kalb-Ramond field, leading to a structure resembling the tensor hierarchy of gauged supergravity.