Dual Double Field Theory

TL;DR

This paper develops a dual formulation of linearized double field theory that includes additional fields beyond previous models, providing a more complete T-duality covariant description of fundamental fields.

Contribution

It introduces a dual double field theory at the linearized level with new fields, clarifying their roles and differences from prior proposals.

Findings

The dual theory encodes fields in mixed Young-tableau representations.

It requires an antisymmetric 2-tensor and a singlet, not all pure gauge.

The additional fields are analogous to phenomena in exotic dualizations.

Abstract

We present the dual formulation of double field theory at the linearized level. This is a classically equivalent theory describing the duals of the dilaton, the Kalb-Ramond field and the graviton in a T-duality or O(D,D) covariant way. In agreement with previous proposals, the resulting theory encodes fields in mixed Young-tableau representations, combining them into an antisymmetric 4-tensor under O(D,D). In contrast to previous proposals, the theory also requires an antisymmetric 2-tensor and a singlet, which are not all pure gauge. The need for these additional fields is analogous to a similar phenomenon for "exotic" dualizations, and we clarify this by comparing with the dualizations of the component fields. We close with some speculative remarks on the significance of these observations for the full non-linear theory yet to be constructed.