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We study supersymmetric $AdS_4\times \Sigma_2$ and $AdS_3\times \Sigma_3$solutions in half-maximal gauged supergravity in six dimensions with$SU(2)_R\times SU(2)$ gauge group. The gauged supergravity is obtained bycoupling three vector multiplets to the pure $F(4)$ gauged supergravity. The$SU(2)_R$ R-symmetry together with the $SO(3)\sim SU(2)$ symmetry of the vectormultiplets are gauged. The resulting gauged supergravity admits supersymmetric$AdS_6$ critical points with $SO(4)\sim SU(2)\times SU(2)$ and $SO(3)\simSU(2)_{\textrm{diag}}$ symmetries. The former corresponds to five-dimensional$N=2$ superconformal field theories (SCFTs) with $E_1\sim SU(2)$ symmetry. Wefind new classes of supersymmetric $AdS_4\times \Sigma_2$ and $AdS_3\times\Sigma_3$ solutions with $\Sigma_{2,3}$ being $S^{2,3}$ and $H^{2,3}$. Thesesolutions describe SCFTs in three and two dimensions obtained from twistedcompactifications of the aforementioned five-dimensional SCFTs with differentnumbers of unbroken supersymmetry and various types of global symmetries.

Twisted compactification of N=2 5D SCFTs to three and two dimensions from F(4) gauged supergravity