dS_5$$ dS5 vacua from matter-coupled 5D $$N=4$$ N=4 gauged supergravity

Abstract We study $$dS_5$$ dS5 vacua within matter-coupled $$N=4$$ N=4 gauged supergravity in five dimensions using the embedding tensor formalism. With a simple ansatz for solving the extremization and positivity of the scalar potential, we derive a set of conditions for the gauged supergravity to admit $$dS_5$$ dS5 as maximally symmetric background solutions. The results provide a new approach for finding $$dS_5$$ dS5 vacua in five-dimensional $$N=4$$ N=4 gauged supergravity and explain a number of notable features pointed out in previous works. These conditions also determine the form of the gauge groups to be $$SO(1,1)\times G_{\text {nc}}$$ SO(1,1)×Gnc with $$G_{\text {nc}}$$ Gnc being a non-abelian non-compact group. In general, $$G_{\text {nc}}$$ Gnc can be a product of SO(1, 2) and a smaller non-compact group $${G^{\prime }}_{{\text {nc}}}$$ G′nc together with (possibly) a compact group. The SO(1, 1) factor is gauged by one of the six graviphotons, that is singlet under $$SO(5)\sim USp(4)$$ SO(5)∼USp(4) R-symmetry. The compact parts of SO(1, 2) and $${G^{\prime }}_{{\text {nc}}}$$ G′nc are gauged by vector fields from the gravity and vector multiplets, respectively. In addition, we explicitly study $$dS_5$$ dS5 vacua for a number of gauge groups and compute scalar masses at the vacua. As in the four-dimensional $$N=4$$ N=4 gauged supergravity, all the $$dS_5$$ dS5 vacua identified here are unstable.