  We study a recently-found class of RG flows in four dimensions exhibiting
enhancement of supersymmetry in the infrared, which provides a lagrangian
description of several strongly-coupled N=2 SCFTs. The procedure involves
starting from a N=2 SCFT, coupling a chiral multiplet in the adjoint
representation of the global symmetry to the moment map of the SCFT and turning
on a nilpotent expectation value for this chiral. In this note we show that,
combining considerations based on 't Hooft anomaly matching and basic results
about the N=2 superconformal algebra, it is possible to understand in detail
the mechanism underlying this phenomenon and formulate a simple criterion for
supersymmetry enhancement which allows us to bypass the analysis with
a-maximization. As a byproduct, we propose an algorithm to identify a
lagrangian UV completion of a given N=2 SCFT under an RG flow of this type,
provided there is one.
