Confinement in a finite duality cascade
We provide several consistency checks of confining dynamics in a recently conjectured holographic dual of a four-dimensional ${\cal N}=1$ supersymmetric gauge theory that flows from a conformal manifold in the UV to a finite set of isolated, fully gapped vacua in the IR. This is obtained by considering D3-branes at the conifold singularity in the presence of an O7-plane, leading to a background where all supergravity fields have a non-trivial profile. We compute holographically the expectation value of a Wilson loop in the fundamental representation and show that it obeys an area law. We then construct the domain walls which interpolate between different vacua in terms of D5-branes wrapping a compact three-cycle of the internal manifold. Their dynamics is governed by the (2+1)-dimensional ${\cal N}=1$ Yang-Mills-Chern-Simons theory predicted by field theory arguments, that reduces in the deep infrared to a TQFT whose inflow action correctly reproduces the mixed anomaly of the four-dimensional theory. Finally, we argue that, unlike in previous models in the literature, axionic strings are unstable in this background. This implies that the corresponding massless axion that would couple to them is absent, in agreement with the fact that the vacua are fully gapped.