We show that certain five-dimensional, $\mathcal{N}=2\mathrm{}$ Yang-Mills-Einstein supergravity theories admit the gauging of the full R-symmetry group, ${\mathrm{SU}\left(2\right)\mathrm{}}_R,$ of the underlying $\mathcal{N}=2\mathrm{}$ Poincaré superalgebra. This generalizes the previously studied Abelian gaugings of ${U\left(1\right)\mathrm{}}_R\subset {\mathrm{SU}\left(2\right)\mathrm{}}_R,$ and completes the construction of the most general vector and tensor field coupled five-dimensional, $\mathcal{N}=2\mathrm{}$ supergravity theories with gauge interactions. The gauging of ${\mathrm{SU}\left(2\right)\mathrm{}}_R$ turns out to be possible only in special cases, and leads to a new type of scalar potential. For a large class of these theories the potential does not have any critical points.

• Received 4 May 2000

DOI:https://doi.org/10.1103/PhysRevD.63.064023