Gauging the full R -symmetry group in five-dimensional, N= 2 Yang-Mills-Einstein-tensor supergravity

We show that certain five-dimensional, N=2 Yang-Mills-Einstein supergravity theories admit the gauging of the full R-symmetry group, SU(2)_R, of the underlying N=2 Poincaré superalgebra. This generalizes the previously studied Abelian gaugings of U(1)_R⊂SU(2)_R, and completes the construction of the most general vector and tensor field coupled five-dimensional, 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.