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!