$$dS_4$$ vacua from matter-coupled 4D $$N=4$$ gauged supergravity

Abstract

AbstractWe study$$dS_4$$dS4vacua within matter-coupled$$N=4$$N=4gauged supergravity in the embedding tensor formalism. We derive a set of conditions for the existence of$$dS_4$$dS4solutions by using a simple ansatz for solving the extremization and positivity of the scalar potential. We find two classes of gauge groups that lead to$$dS_4$$dS4vacua. One of them consists of gauge groups of the form$$G_{\text {e}}\times G_{\text {m}}\times H$$Ge×Gm×HwithHbeing a compact group and$$G_{\text {e}}\times G_{\text {m}}$$Ge×Gma non-compact group with$$SO(3)\times SO(3)$$SO(3)×SO(3)subgroup and dyonically gauged. These gauge groups are the same as those giving rise to maximally supersymmetric$$AdS_4$$AdS4vacua. The$$dS_4$$dS4and$$AdS_4$$AdS4vacua arise from different coupling ratios between$$G_{\text {e}}$$Geand$$G_{\text {m}}$$Gmfactors. Another class of gauge groups is given by$$SO(2,1)_{\text {e}}\times SO(2,1)_{\text {m}}\times G_{\text {nc}}\times G'_{\text {nc}}\times H$$SO(2,1)e×SO(2,1)m×Gnc×Gnc′×HwithSO(2, 1),$$G_{\text {nc}}$$Gncand$$G'_{\text {nc}}$$Gnc′dyonically gauged. We explicitly check that all known$$dS_4$$dS4vacua in$$N=4$$N=4gauged supergravity satisfy the aforementioned conditions, hence the two classes of gauge groups can accommodate all the previous results on$$dS_4$$dS4vacua in a simple framework. Accordingly, the results provide a new approach for finding$$dS_4$$dS4vacua. In addition, relations between the embedding tensors for gauge groups admitting$$dS_4$$dS4and$$dS_5$$dS5vacua are studied, and a new gauge group,$$SO(2,1)\times SO(4,1)$$SO(2,1)×SO(4,1), with a$$dS_4$$dS4vacuum is found by applying these relations to$$SO(1,1)\times SO(4,1)$$SO(1,1)×SO(4,1)gauge group in five dimensions.