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

TL;DR

The paper demonstrates that certain 5D, N=2 Yang-Mills/Einstein/tensor supergravity theories admit gauging of the full R-symmetry group $SU(2)_R$, via a diagonal gauging with a suitable $K \supset SU(2)_G$. The authors construct the corresponding Lagrangian and SUSY transformation rules, introducing a new scalar potential term $P^{(R)}(\varphi)$ and deriving the necessary supersymmetry-consistent constraints. Analyzing three symmetric-space families (generic Jordan, magical Jordan, and generic non-Jordan), they show that the total scalar potential $P_{tot}=P+P^{(R)}$ typically lacks critical points, indicating no vacua in the physically allowed region and highlighting the rigidity of $SU(2)_R$ gaugings relative to $U(1)_R$ gaugings. The results have implications for AdS/CFT applications and RS-like embeddings, clarifying the landscape of admissible vacua in these more general matter-coupled supergravity theories.

Abstract

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 Poincare superalgebra. This generalizes the previously studied Abelian gaugings of U(1)_R subgroup of 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.