Argyres-Douglas CFT Adding of mass in supersymmetric gauge theories will affect structure of moduli space by creating new singular point (picture and some statements from Matteo Bertolini: Lectures on Supersymmetry):

Novel phenomenon which can occur when the gauge group rank n > 1 and/or when matter is added: the existence of special points on the moduli space, known as Argyres-Douglas points, where the theory enjoys an interacting (as opposed to free) conformal phase  (this CFT haven't Lagrangian description!).
Physically, this corresponds to mutually non-local objects (see this), as e.g. a dyon and a monopole, or a dyon and an electrically charged object, becoming simultaneously massless.
I have some questions, related Argyres-Douglas theory, that describe such interacting CFT.
1) Why Argyres-Douglas points correspondence to CFT? Is this related to mutually non-locality of of emergent massless objects? How we lose all dimension parameters in such points?
2) Which RG flow have this points as fixed?
3) Also I here that this theory is in strong coupling, and so haven't Lagrangian description. How to understand, that this theories in strong coupling? What can we now say about this theories??
I will be very appreciate for answers!
 A: The $SU(N)$ gauge theory with $\mathcal{N} = 2$ SUSY and $F$ hypermultiplets in 
  fundamental representation has $\beta$ function
$$\beta(g) = \frac{g^3}{16\pi^2} (F-2N)$$
One trivial set of fixed points which can be seen is $F=2N$, which doesn't 
   depend on the coupling.
Now consider that there are two species of massless particles, one is electrically charged and one is magnetically charged at the same point in the moduli space of the $\mathcal{N} =2$ gauge theory. The renormalization of the coupling from the electric charge drives the IR coupling to zero, while renormalization from the magnetic charge drives the IR coupling to $\infty$. For an appropriate set of charges, it was first pointed out by Argyres and Douglas for $SU(3)$ gauge theories (and later others for SU(2) etc.)  that the IR coupling flows to an IR fixed point. Since this is a fixed point with $\beta =0$, its a CFT. For the specifics of the RG flow, have a look at the linked paper.
Since this is a CFT, one can understand features of this theory even without a Lagrangian description, using the CFT data (scaling dimensions and the OPE coefficients) (See Conformal Bootstrap). You start with the CFT data, and can "solve" the CFT as you can calculate all possible correlation functions.
