Gaugings of N=4 three dimensional gauged supergravity with exceptional coset manifolds

Abstract

Some admissible gauge groups of N=4 Chern-Simons gauged supergravity in three dimensions with exceptional scalar manifolds $G_{2(2)}/SO(4)$, $F_{4(4)}/USp(6)\times SU(2)$, $E_{6(2)}/SU(6)\times SU(2)$, $E_{7(-5)}/SO(12)\times SU(2)$ and $E_{8(-24)}/E_7\times SU(2)$ are identified. In particular, a complete list of all possible gauge groups is given for the theory with $G_{2(2)}/SO(4)$ coset space. We also study scalar potentials for all of these gauge groups and find some critical points. In the case of $F_{4(4)}/USp(6)\times SU(2)$ target space, we give some semisimple gauge groups which are maximal subgroups of $F_{4(4)}$. Most importantly, we construct the $SO(4)\ltimes \mathbf{T}^6$ gauged supergravity which is equivalent to N=4 SO(4) Yang-Mills gauged supergravity. The latter is proposed to be obtained from an $S^3$ reduction of $(1,0)$ six dimensional supergravity coupled to two vector and two tensor multiplets. The scalar potential of this theory on the scalar fields which are invariant under SO(4) is explicitly computed. Depending on the value of the coupling constants, the theory admits both dS and AdS vacua when all of the 28 scalars vanish. The maximal N=4 supersymmetric $AdS_3$ should correspond to the $AdS_3\times S^3$ solution of the $(1,0)$ six dimensional theory. Finally, some gauge groups of the theories with $E_{6(2)}/SU(6)\times SU(2)$, $E_{7(-5)}/SO(12)\times SU(2)$ and $E_{8(-24)}/E_7\times SU(2)$ scalar manifolds are identified.