Consistent truncations of supergravity and $\frac{1}{2}$-BPS RG flows in $4d$ SCFTs

With the purpose of holographically describing flows from a large family of four dimensional ${\cal N}=1$ and ${\cal N}=2$ conformal field theories, we discuss truncations of seven dimensional supergravity to five dimensions. We write explicitly the reduced gauged supergravity and find BPS equations for simple configurations. Lifting these flows to eleven dimensions or Massive IIA supergravity, we present string duals to RG flows from strongly coupled conformal theories when deformed by marginal and/or relevant operators. We further discuss observables common to infinite families of ${\cal N}=1$ and ${\cal N}=2$ QFTs in this context.