Conformal manifolds and 3d mirrors of (Dn, Dm) theories

The Argyres-Douglas (AD) theories of type (D-n, D-m), realized by type IIB geometrical engineering on a single hypersurface singularity, are studied. We analyze their conformal manifolds and propose the 3d mirror theories of all theories in this class upon reduction on a circle. A subclass of the AD theories in question that admits marginal couplings is found to be SO or USp gaugings of certain D-p(SO(2N)) and D-p(USp(2N)) theories. For such theories, we develop a method to derive this weakly-coupled description from the Newton polygon associated to the singularity. We further find that the presence of crepant resolutions of the geometry is reflected in the presence of a (non-abelian) symplectic-type gauge node in the quiver description of the 3d mirror theory. The other important results include the 3d mirrors of all D-p(SO(2N)) theories, as well as certain properties of the D-p(USp(2N)) theories that admit Lagrangian descriptions.