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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 typeinvolving irregular punctures of regular semi-simple type. The 11d supergravityduals contain an internal space of the form of a fibered product of a disc witha squashed and fibered four-sphere and includes orbifold projections whichdepend on the type of twist lines/outer-automorphism twists in the class$\mathcal{S}$ theory. We verify the holographic duality by determining andmatching the anomalies (including the central charges $a$ and $c$ and theflavor central charges) at leading and subleading orders. The Higgs branch ofthe conformal field theory is described via Higgsing by a nilpotent orbit of aclassical Lie algebra; we find the exact closed form formulae for the centralcharges for every Higgsing. We prove that in the supergravity duals,constraints on the type of partitions associated to allowable Higgsings areenforced by the consistency condition known as the t-rule.

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