DS_4 vacua from matter-coupled 4D N=4 gauged supergravity

Abstract

We study dS_4 vacua within matter-coupled N=4 gauged supergravity in the embedding tensor formalism. We derive a set of conditions for the existence of dS_4 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 dS_4 vacua. One of them consists of gauge groups of the form G_{text {e}}times G_{text {m}}times H with H being a compact group and G_{text {e}}times G_{text {m}} a non-compact group with SO(3)times SO(3) subgroup and dyonically gauged. These gauge groups are the same as those giving rise to maximally supersymmetric AdS_4 vacua. The dS_4 and AdS_4 vacua arise from different coupling ratios between G_{text {e}} and G_{text {m}} factors. 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 with SO(2, 1), G_{text {nc}} and G'_{text {nc}} dyonically gauged. We explicitly check that all known dS_4 vacua in N=4 gauged supergravity satisfy the aforementioned conditions, hence the two classes of gauge groups can accommodate all the previous results on dS_4 vacua in a simple framework. Accordingly, the results provide a new approach for finding dS_4 vacua. In addition, relations between the embedding tensors for gauge groups admitting dS_4 and dS_5 vacua are studied, and a new gauge group, SO(2,1)times SO(4,1), with a dS_4 vacuum is found by applying these relations to SO(1,1)times SO(4,1) gauge group in five dimensions.