Consistent KK truncations for M5-branes wrapped on Riemann surfaces

We construct a consistent Kaluza-Klein reduction of $D=11$ supergravity on $Sigma_2times S^4$, where $Sigma_2=S^2,mathbb{R}^2$ or $H^2$, or a quotient thereof, at the level of the bosonic fields. The result is a gauged $N=4$, $D=5$ supergravity theory coupled to three vector multiplets, with the gauging lying in an $SO(2)times SE(3)subset SO(5,3)$ subgroup of the $SO(1,1)times SO(5,3)$ global symmetry group of the ungauged theory. For $Sigma_2=H^2$, the $D=5$ theory has a maximally supersymmetric $AdS_5$ vacuum which uplifts to the known solution of $D=11$ supergravity corresponding to M5-branes wrapping a Riemann surface with genus greater than one and dual to an $N=2$ SCFT in $d=4$. For $Sigma_2=S^2$, we find two $AdS_5$ solutions, one of which is new, and both of which are unstable. There is an additional subtruncation to an $N=2$ gauged supergravity coupled to two vector multiplets, with very special real manifold $SO(1,1)times SO(1,1)$, and a single hypermultiplet, with quaternionic Kahler manifold $SU(2,1)/S[U(2)times U(1)]$ and gauging associated with an $SO(2)timesmathbb{R}subset SU(2,1)$ subgroup.