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

TL;DR

This paper analyzes the critical points of potentials in 5d, N=2 gauged supergravity theories with tensor multiplets, revealing new types of ground states including anti-de Sitter and de Sitter solutions.

Contribution

It identifies novel critical points in these supergravity theories caused by tensor multiplets, expanding understanding of their vacuum structure.

Findings

Tensor contributions can change extrema from maxima to saddle points.

New critical points include anti-de Sitter and de Sitter vacua.

Analysis applies to a broad class of N=2 gauged supergravity theories.

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).