| Summary: | Argyres-Douglas theories constitute an important class of superconformal field theories in 4d. The main focus of this paper is on two infinite families of such theories, known as Dbp(SO(2N)) and (Am, Dn). We analyze in depth their conformal manifolds. In doing so we encounter several theories of class 𝒮 of twisted Aodd, twisted Aeven and twisted D types associated with a sphere with one twisted irregular puncture and one twisted regular puncture. These models include Dp(G) theories, with G non-simply-laced algebras. A number of new properties of such theories are discussed in detail, along with new SCFTs that arise from partially closing the twisted regular puncture. Moreover, we systematically present the 3d mirror theories, also known as the magnetic quivers, for the Dbp(SO(2N)) theories, with p ≥ b, and the (Am, Dn) theories, with arbitrary m and n. We also discuss the 3d reduction and mirror theories of certain Dbp(SO(2N)) theories, with p < b, where the former arises from gauging topological symmetries of some Tσp[SO(2M)] theories that are not manifest in the Lagrangian description of the latter.
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