Five-branes wrapped on topological disks from 7D N=2 gauged supergravity

We study supersymmetric $AdS_5\times \Sigma$ solutions, for $\Sigma$ being a topological disk with non-trivial $U(1)$ holonomy at the boundary or "half-spindle", in seven-dimensional $N=2$ gauged supergravity coupled to three vector multiplets. We consider compact and non-compact gauge groups, $SO(4-p,p)$, for $p=0,1,2$, and find a number of $AdS_5\times \Sigma$ solutions with $SO(2)\times SO(2)$ and $SO(2)_{\text{diag}}$ residual symmetry from $SO(4)$ and $SO(2,2)$ gauge groups. We also find an $SO(2)_R\subset SO(3)_R\sim SU(2)_R$ symmetric solution which can be regarded as a solution of pure $N=2$ gauged supergravity with $SO(3)_R$ gauge group and all the fields from vector multiplets vanishing. The solutions preserve $\frac{1}{2}$ of the original $N=2$ supersymmetry and could be interpreted as supergravity duals of $N=1$ superconformal field theories in four dimensions. In particular, some of these solutions can be embedded in ten or eleven dimensions in which a description in terms of five-branes wrapped on a topological disk can be given.