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

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 $SO(4)\sim SO(3)\times SO(3)$symmetryandadmitstwo$N=2$supersymmetric$AdS_7$vacuawith$SO(4)$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.