  In a recent paper, we proposed closed-form expressions for the superconformal
indices of the (A_1, A_{2n-3}) and (A_1, D_{2n}) Argyres-Douglas (AD)
superconformal field theories (SCFTs) in the Schur limit. Following up on our
results, we turn our attention to the small S^1 regime of these indices. As
expected on general grounds, our study reproduces the S^3 partition functions
of the resulting dimensionally reduced theories. However, we show that in all
cases---with the exception of the reduction of the (A_1, D_4) SCFT---certain
imaginary partners of real mass terms are turned on in the corresponding mirror
theories. We interpret these deformations as R symmetry mixing with the
topological symmetries of the direct S^1 reductions. Moreover, we argue that
these shifts occur in any of our theories whose four-dimensional N=2
superconformal U(1)_R symmetry does not obey an SU(2) quantization condition.
We then use our R symmetry map to find the four-dimensional ancestors of
certain three-dimensional operators. Somewhat surprisingly, this picture turns
out to imply that the scaling dimensions of many of the chiral operators of the
four-dimensional theory are encoded in accidental symmetries of the
three-dimensional theory. We also comment on the implications of our work on
the space of general N=2 SCFTs.
