We discuss the field theory of 3-brane probes in F-theory compactifica
tions in two configurations, generalizing the work of Sen and of Banks
, Douglas and Seiberg. One configuration involves several parallel 3-b
rane probes in F-theory compactified on T-4/Z(2), while the other invo
lves a compactification of F-theory on T-6/Z(2) x Z(2) (which includes
intersecting D-4 singularities). In both cases string theory provides
simple pictures of the space-time theory, whose implications for the
3-brane world-volume theories are discussed. In the second case the fi
eld theory on the probe is an unusual N = 1 superconformal theory, wit
h exact electric-magnetic duality. Several open questions remain conce
rning the description of this theory. (C) 1997 Published by Elsevier S
cience B.V.