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 $T^6 / Z_2 \times Z_2$ (which includes intersecting D_4 singularities). In both cases string theory provides simple pictures of the spacetime theory, whose implications for the three-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 SL(2,Z) electric-magnetic duality. Several open questions remain concerning the description of this theory.