  We discuss models with no dynamical vector fields in various dimensions which
we claim might have exceptional symmetry on some loci of their parameter space.
In particular we construct theories with four supercharges flowing to theories
with global symmetry enhancing to $F_4$, $E_6$, and $E_7$. The main evidence
for these claims is based on extracting information about the symmetry
properties of the theories from their supersymmetric partition functions.
