4d N=1/2d $$ \mathcal{N}=1/2d $$ Yang-Mills duality in holography

Abstract We study the supergravity dual of four-dimensional N=1 $$ \mathcal{N}=1 $$ superconformal field theories arising from wrapping M5-branes on a Kähler 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 AdS7 and AdS5 as well as between different AdS5 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