  We analyze the N=2 superconformal field theories that arise when a pair of
D3-branes probe an F-theory singularity from the perspective of the associated
vertex operator algebra. We identify these vertex operator algebras for all
cases; we find that they have a completely uniform description, parameterized
by the dual Coxeter number of the corresponding global symmetry group. We
further present free field realizations for these algebras in the style of
recent work by three of the authors. These realizations transparently reflect
the algebraic structure of the Higgs branches of these theories. We find
fourth-order linear modular differential equations for the vacuum
characters/Schur indices of these theories, which are again uniform across the
full family of theories and parameterized by the dual Coxeter number. We
comment briefly on expectations for the still higher-rank cases.
