Coordinate-Transformation Formulation for Gauged Supergravity Deformations

Establish whether the non-abelian uni-vector deformations of gauged supergravities introduced through the double field theory generalized-metric transformation can be reformulated as diffeomorphisms in the full doubled space.

Background

The paper proves that the corresponding non-abelian uni-vector deformations in the non-abelian Einstein–Maxwell theories admit an interpretation as coordinate transformations in the extended space of the parent general relativity theory. For gauged supergravities, however, the deformation acts on the generalized metric through an O($\mathfrak d+\mathfrak n$,$\mathfrak d+\mathfrak n$) matrix within the double field theory framework.

The conclusion explicitly distinguishes the unresolved gauged-supergravity case from the Einstein–Maxwell case: although the deformation matrix is simple, its realization as a diffeomorphism of the complete doubled space has not been obtained. Resolving this problem would provide a geometric interpretation of the gauged-supergravity deformations analogous to the one established for the parent general-relativity construction.