D4-branes wrapped on topological disks from matter-coupled F(4) gauged supergravity

We study a number of supersymmetric $AdS_4\times Σ$ solutions with $Σ$ being a topological disk with non-trivial $U(1)$ holonomy on the boundary or a ``half-spindle'' from matter-coupled $F(4)$ gauged supergravity. The gauged supergravity is coupled to three vector multiplets with $SO(3)\times SO(3)$ gauge group. The resulting solutions preserve eight supercharges and $SO(2)\times SO(2)$ or $SO(2)_{\text{diag}}$ symmetries and are expected to be dual to $N=2$ SCFTs in three dimensions arising from compactifications of five-dimensional $N=2$ SCFT on a half-spindle. All of the solutions lie within the $U(1)\times U(1)$ subsector of the matter-coupled $F(4)$ gauged supergravity that can be embedded in massive type IIA theory. After uplifted to ten dimensions, the solutions can be interpreted as a system of D4-D8-branes wrapped on $Σ$. Some of the solutions are asymptotic to a locally $AdS_6$ geometry and can be identified as codimension-2 conformal defects within the $N=2$ SCFT in five dimensions. For these solutions, the circle inside $Σ$ decompactifies in the $AdS_6$ limit rendering the holographic free energy infinite. There also exist solutions with finite free energy in the dual three-dimensional SCFTs. In addition, we show that the results both extend the previously known solutions and provide a novel class of solutions.