  N=(2,2) theories in 1+1D exhibit a direct correspondence between the
R-charges of chiral operators at a conformal point and the multiplicities of
BPS kinks in a massive deformation, as shown by Cecotti and Vafa. We obtain an
analogous relation in 3+1D for N=2 gauge theories that are massive
perturbations of Argyres-Douglas fixed points, utilizing the geometric
engineering approach to N=2 vacua within IIB string theory. In this case the
scaling dimensions of a certain subset of chiral operators at the UV fixed
point are related to the multiplicities of BPS dyons. When the Argyres-Douglas
SCFT is realized at the root of a baryonic Higgs branch, this translation from
1+1D to 3+1D can be understood physically from the relation between the bulk
dynamics and the N=(2,2) worldsheet dynamics of vortices in the baryonic Higgs
phase. Under a relevant perturbation, the BPS kink multiplicity on the vortex
worldsheet translates to that of the bulk dyonic states. The latter viewpoint
suggests the 3+1D version of the Cecotti-Vafa relation may hold more generally,
and simple tests provide evidence in favor of this for more generic choices of
the baryonic root.
