Gauging the Full R-Symmetry Group in Five-dimensional, N = 2 Yang-Mills/Einstein/tensor Supergravity

We show that certain 5d, N=2 Yang-Mills/Einstein supergravity theories admit the gauging of the \emph{full} R-symmetry group, $SU(2)_{R}$, of the underlying $\mathcal{N}=2$ Poincar\'{e} superalgebra. This generalizes the previously studied Abelian gaugings of $U(1)_{R}\subset SU(2)_{R}$, and completes the construction of the most general vector and tensor field coupled $5d$, $\mathcal{N}=2$ supergravity theories with gauge interactions. The gauging of $SU(2)_{R}$ 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.