We argue that in theories of quantum gravity with discrete gauge symmetries, e.g. Z k , the gauge couplings of U(1) gauge symmetries become weak in the limit of large k, as g → k −α with α a positive order 1 coefficient. The conjecture is based on black hole arguments combined with the Weak Gravity Conjecture (or the BPS bound in the supersymmetric setup), and the species bound. We provide explicit examples based on type IIB on AdS 5 × S 5 /Z k orbifolds, and M-theory on AdS 4 × S 7 /Z k ABJM orbifolds (and their type IIA reductions). We study AdS 4 vacua of type IIA on CY orientifold compactifications, and show that the parametric scale separation in certain infinite families is controlled by a discrete Z k symmetry for domain walls. We accordingly propose a refined version of the strong AdS Distance Conjecture, including a parametric dependence on the order of the discrete symmetry for 3-forms.

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 $$ {D}_p^b $$ D p b (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 $$ {D}_p^b $$ D p b (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 $$ {D}_p^b $$ D p b (SO(2N)) theories, with p < b, where the former arises from gauging topological symmetries of some $$ {T}_p^{\sigma } $$ T p σ [SO(2M)] theories that are not manifest in the Lagrangian description of the latter.