Field theory questions for string theory answers

We discuss the field theory of 3-brane probes in F-theory compactifications in two configurations, generalizing the work of Sen and of Banks, Douglas and Seiberg. One configuration involves several parallel 3-brane probes in F-theory compactified on T-4/Z(2), while the other involves 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 field theory on the probe is an unusual N = 1 superconformal theory, with exact electric-magnetic duality. Several open questions remain concerning the description of this theory. (C) 1997 Published by Elsevier Science B.V.