The Vacua of 5d,N=2 Gauged Yang-Mills/Einstein/Tensor Supergravity: Abelian Case

TL;DR

The paper analyzes the vacua of 5d, N=2 gauged YM/Einstein supergravity with tensor multiplets, focusing on the Abelian case with scalar manifold $SO(1,1)\times SO(2,1)/SO(2)$. It shows that tensor contributions modify the SUSY extrema and create novel AdS/dS vacua not seen in tensor-free models, with detailed results for the $U(1)_{R}\times SO(2)$ and $U(1)_{R}\times SO(1,1)$ gaugings, including one-parameter families of Minkowski, AdS, and de Sitter vacua depending on the gauging parameters. The analysis extends to the generic Jordan-family theories with scalar manifolds $SO(1,1)\times SO(n-1,1)/SO(n-1)$, revealing a rich vacuum structure arising from the interplay of $P$ and $P^{(R)}$ in the total potential $P_{ ext{tot}}=P+\lambda P^{(R)}$, where $\lambda=g_R^2/g^2$. Overall, tensor multiplets enlarge the landscape of supersymmetric and non-supersymmetric vacua and motivate further study of more general gauge groups and tensor couplings. $P_{ ext{tot}}$ and its critical points are central, with $P$ potentially turning SUSY maxima into saddles and producing qualitatively new ground states in AdS and de Sitter geometries.

Abstract

We give a detailed study of the critical points of the potentials of the simplest non-trivial N=2 gauged Yang-Mills/Einstein supergravity theories with tensor multiplets. The scalar field target space of these examples is SO(1,1)XSO(2,1)/SO(2). The possible gauge groups are SO(2)XU(1)_R and SO(1,1)XU(1)_R, where U(1)_R is a subgroup of the R-symmetry group SU(2)_R, and SO(2) and SO(1,1) are subgroups of the isometry group of the scalar manifold. The scalar potentials of these theories consist of a contribution from the U(1)_R gauging and a contribution that is due to the presence of the tensor fields. We find that the latter contribution can change the form of the supersymmetric extrema from maxima to saddle points. In addition, it leads to novel critical points not present in the corresponding gauged Yang-Mills/Einstein supergravity theories without the tensor multiplets. For the SO(2)XU(1)_R gauged theory these novel critical points correspond to anti-de Sitter ground states. For the non-compact SO(1,1)XU(1)_R gauging, the novel ground states are de Sitter. The analysis of the critical points of the potential carries over in a straightforward manner to the generic family of N=2 gauged Yang-Mills/Einstein supergravity theories coupled to tensor multiplets whose scalar manifolds are of the form SO(1,1)XSO(n-1,1)/SO(n-1).