Stable de Sitter Vacua in 4 Dimensional Supergravity Originating from 5 Dimensions

TL;DR

This work shows how stable de Sitter vacua in four-dimensional $ ext{N}=2$ supergravity can originate from five-dimensional theories via dimensional reduction. Central to the construction are (i) gauging non-compact symmetries like $SO(1,1)$ together with a compatible $R$-symmetry factor, (ii) a carefully chosen holomorphic (symplectic) section in 4D, and (iii) a group contraction that renders the potential positive-definite in the reduced theory. By combining tensor, $R$-symmetry, and (optionally) hypermultiplet gaugings, and employing de Roo-Wagemans rotations (dRW) and GMZ symplectic rotations, the authors produce explicit stable dS vacua in 4D for several setups, including $R_s=U(1)_R$, $R_s=SU(2)_R$, and with a universal hypermultiplet. They also show that contracted five-dimensional gaugings can descend to direct four-dimensional models that retain stability, linking 5D and 4D theories in a concrete way. The results extend the landscape of 4D de Sitter vacua to more general homogeneous scalar manifolds and provide pathways for future string-theory embeddings and phenomenological applications.

Abstract

The five dimensional stable de Sitter ground states in N=2 supergravity obtained by gauging SO(1,1) symmetry of the real symmetric scalar manifold (in particular a generic Jordan family manifold of the vector multiplets) simultaneously with a subgroup R_s of the R-symmetry group descend to four dimensional de Sitter ground states under certain conditions. First, the holomorphic section in four dimensions has to be chosen carefully by using the symplectic freedom in four dimensions; and second, a group contraction is necessary to bring the potential into a desired form. Under these conditions, stable de Sitter vacua can be obtained in dimensionally reduced theories (from 5D to 4D) if the semi-direct product of SO(1,1) with R^(1,1) together with a simultaneous R_s is gauged. We review the stable de Sitter vacua in four dimensions found in earlier literature for N=2 Yang-Mills Einstein supergravity with SO(2,1) x R_s gauge group in a symplectic basis that comes naturally after dimensional reduction. Although this particular gauge group does not descend directly from five dimensions, we show that, its contraction does. Hence, two different theories overlap in certain limits. Examples of stable de Sitter vacua are given for the cases: (i) R_s=U(1)_R, (ii) R_s=SU(2)_R, (iii) N=2 Yang-Mills/Einstein Supergravity theory coupled to a universal hypermultiplet. We conclude with a discussion regarding the extension of our results to supergravity theories with more general homogeneous scalar manifolds.

Figures (2)

• Figure 1: Examples of de Sitter extrema in supergravity theories: (a) Stable minima with a flat direction. The potential belongs to the $4D,\mathcal{N}=2$ supergravity coupled to 3 vector multiplets, considered in FTP02. Figure taken from FTP03. (b) Saddle point, where the scalar rolls into a Minkowski minimum on one side and anti-de Sitter minimum on the other. This is $4D,\mathcal{N}=2$ supergravity coupled to 1 hypermultiplet, considered in BM03. The potential includes instanton corrections.
• Figure 2: The extrema of the potential $P_{(5)}(R,\theta)$ due to $SO(1,1)\times U(1)_R$ gauging, evaluated at $\varphi^4=0$; $V_1=0$ and $\lambda=1$; with parametrization $\varphi^2 = R\, \cosh\theta,\,\varphi^3 = R\, \sinh\theta$. The zero eigenvalue of the Hessian corresponds to the flat direction of the potential at its minima.