dS4 vacua from matter-coupled 4D N= 4 gauged supergravity

Abstract

We study dS4 vacua within matter-coupled N= 4 gauged supergravity in the embedding tensor formalism. We derive a set of conditions for the existence of dS4 solutions 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 dS4 vacua. One of them consists of gauge groups of the form Ge× Gm× H with H being a compact group and Ge× Gm a non-compact group with SO(3) × SO(3) subgroup and dyonically gauged. These gauge groups are the same as those giving rise to maximally supersymmetric AdS4 vacua. The dS4 and AdS4 vacua arise from different coupling ratios between Ge and Gm factors. Another class of gauge groups is given by SO(2,1)e×SO(2,1)m×Gnc×Gnc?×H with SO(2, 1), Gnc and Gnc? dyonically gauged. We explicitly check that all known dS4 vacua in N= 4 gauged supergravity satisfy the aforementioned conditions, hence the two classes of gauge groups can accommodate all the previous results on dS4 vacua in a simple framework. Accordingly, the results provide a new approach for finding dS4 vacua. In addition, relations between the embedding tensors for gauge groups admitting dS4 and dS5 vacua are studied, and a new gauge group, SO(2 , 1) × SO(4 , 1) , with a dS4 vacuum is found by applying these relations to SO(1 , 1) × SO(4 , 1) gauge group in five dimensions. © 2019, The Author(s).