De Sitter vacua from N=2 gauged supergravity

TL;DR

The paper addresses the challenge of realizing controlled de Sitter vacua in $N=2$ gauged supergravity by incorporating quantum corrections into the universal hypermultiplet moduli space, described by the Calderbank-Pedersen quaternionic metric with $U(1)\times U(1)$ isometries. By Abelian gauging two isometries and deriving the superpotential $W$ and scalar potential $V$ from the Killing data, the authors construct a potential with two supersymmetric minima connected by a de Sitter saddle, with a possible flat SUSY minimum and a negative pole that constrains the flow. The analysis relies on a 3-pole solution for $F(\rho,\eta)$ encoding instanton corrections and yields explicit fixed points at $r=0$, $\theta=\pm\tfrac{\pi}{2}$ after a coordinate change $\rho = \sinh r \cos\theta$, $\eta = \cosh r \sin\theta$. The results illuminate a concrete mechanism for dS vacua in four- and five-dimensional $N=2$ gauged supergravity, with potential implications for cosmology and holography, including locked-inflation scenarios and connections to RG flows in the dual theory.

Abstract

Typical de Sitter (dS) vacua of gauged supergravity correspond to saddle points of the potential and often the unstable mode runs into a singularity. We explore the possibility to obtain dS points where the unstable mode goes on both sides into a supersymmetric smooth vacuum. Within N=2 gauged supergravity coupled to the universal hypermultiplet, we have found a potential which has two supersymmetric minima (one of them can be flat) and these are connected by a de Sitter saddle point. In order to obtain this potential by an Abelian gauging, it was important to include the recently proposed quantum corrections to the universal hypermultiplet sector. Our results apply to four as well as five dimensional gauged supergravity theories.

Figures (1)

• Figure 1: For this plot we have chosen $a=5$ , $b =-1$ , $c=0.1$ . It shows one AdS minimum at $(r, \theta) = (0, -{\pi \over 2})$, a flat space vacuum at $(r, \theta) = (0, {\pi \over 2})$ and in-between there is a deSitter saddle point.