Holographic duals of Higgsed $\mathcal{D}_p^b(BCD)$

We construct the AdS$_5$ holographic duals to all non-Lagrangian 4d $\mathcal{N}=2$ superconformal field theories of Argyres--Douglas type, namely, $\mathcal{D}_p^{\,b}(G)$, arising from class $\mathcal{S}$ of classical type involving irregular punctures of regular semi-simple type. The 11d supergravity duals contain an internal space of the form of a fibered product of a disc with a squashed and fibered four-sphere and includes orbifold projections which depend on the type of twist lines/outer-automorphism twists in the class $\mathcal{S}$ theory. We verify the holographic duality by determining and matching the anomalies (including the central charges $a$ and $c$ and the flavor central charges) at leading and subleading orders. The Higgs branch of the conformal field theory is described via Higgsing by a nilpotent orbit of a classical Lie algebra; we find the exact closed form formulae for the central charges for every Higgsing. We prove that in the supergravity duals, constraints on the type of partitions associated to allowable Higgsings are enforced by the consistency condition known as the t-rule.