Abstract
We study orbifolds of 
= 4 U(n) super-Yang-Mills theory
given by discrete subgroups of SU(2) and SU(3).
We have reached many interesting observations that have
graph-theoretic interpretations. For the subgroups of SU(2), we have
shown how the matter content agrees with current quiver theories
and have offered a possible explanation. In the case of SU(3) we have
constructed
a catalogue of candidates for finite (chiral) = 1 theories, giving
the gauge group and matter content. Finally, we
conjecture a McKay-type correspondence for Gorenstein singularities in
dimension 3 with modular invariants of WZW conformal models.
This implies a connection between a class of finite = 1 supersymmetric
gauge theories in four dimensions and
the classification of affine SU(3) modular invariant partition functions
in two dimensions.