  We consider field theories arising from a large number of D3-branes near
singularities in F-theory. We study the theories at various conformal points,
and compute, using their conjectured string theory duals, their large $N$
spectrum of chiral primary operators. This includes, as expected, operators of
fractional conformal dimensions for the theory at Argyres-Douglas points.
Additional operators, which are charged under the (sometimes exceptional)
global symmetries of these theories, come from the 7-branes. In the case of a
$D_4$ singularity we compare our results with field theory and find agreement
for large $N$. Finally, we consider deformations away from the conformal
points, which involve finding new supergravity solutions for the geometry
produced by the 3-branes in the 7-brane background. We also discuss 3-branes in
a general background.
