  D3-branes are often a necessary ingredient in global compactifications of
F-theory. In minimal realizations of flavor hierarchies in F-theory GUT models,
suitable fluxes are turned on, which in turn attract D3-branes to the Yukawa
points. Of particular importance are ``E-type'' Yukawa points, as they are
required to realize a large top quark mass. In this paper we study the
worldvolume theory of a D3-brane probing such an E-point. D3-brane probes of
isolated exceptional singularities lead to strongly coupled N = 2 CFTs of the
type found by Minahan and Nemeschansky. We show that the local data of an
E-point probe theory determines an N = 1 deformation of the original N = 2
theory which couples this strongly interacting CFT to a free hypermultiplet.
Monodromy in the seven-brane configuration translates to a novel class of
deformations of the CFT. We study how the probe theory couples to the Standard
Model, determining the most relevant F-term couplings, the effect of the probe
on the running of the Standard Model gauge couplings, as well as possible
sources of kinetic mixing with the Standard Model.
