Supersymmetric solutions from matter-coupled 7D N=2 gauged supergravity

Abstract

We study supersymmetric solutions within seven-dimensional $N=2$ gauged supergravity coupled to three vector multiplets in seven dimensions. The gauged supergravity contains six vector fields that gauge the $SO(4)\sim SO(3)\times SO(3)$ symmetry and admits two $N=2$ supersymmetric $Ad{S}_7$ vacua with $SO(4)$ and $SO(3{)}_{\text{diag}}\subset SO(3)\times SO(3)$ symmetries. We consider solutions interpolating between two asymptotically locally $Ad{S}_7$ geometries in the presence of a three-form field. For a particular value of the two $SO(3)$ gauge coupling constants, the $SO(3{)}_{\text{diag}}$ supersymmetric $Ad{S}_7$ vacuum does not exist, but the solutions can be uplifted to eleven dimensions by a known reduction ansatz. We also study solutions of this type and their embedding in M-theory. We further extend these solutions to include the $SO(3{)}_{\text{diag}}$ gauge fields and argue that, in general, this generalization does not lead to supersymmetric solutions.

22 pages, no figure, typos corrected, minor changes