  We study the supergravity dual of four-dimensional ${\mathcal{N}=1}$
superconformal field theories arising from wrapping M5-branes on a K\"ahler
two-cycle inside a Calabi-Yau threefold. We derive an effective
three-dimensional theory living on the cobordism between the infrared and
ultraviolet Riemann surfaces, describing the renormalization group flows
between AdS$_7$ and AdS$_{5}$ as well as between different AdS$_{5}$ fixed
points. The realization of this system as an effective theory is convenient to
make connections to known theories, and we show that upon imposing (physical)
infrared boundary conditions, the effective three-dimensional theory further
reduces to two-dimensional $SU(2)$ Yang-Mills theory on the Riemann surface,
thus deriving a correspondence between the gravity duals of a class of
$\mathcal{N}=1$ superconformal field theories arising from wrapping M5-branes
on a Riemann surface and two-dimensional Yang-Mills theory on the same Riemann
surface.
