We explore some curious implications of Seiberg duality for an SU(2)
four-dimensional gauge theory with eight chiral doublets. We argue that two
copies of the theory can be deformed by an exactly marginal quartic
superpotential so that they acquire an enhanced E7 flavor symmetry. We argue
that a single copy of the theory can be used to define an E7-invariant
superconformal boundary condition for a theory of 28 five-dimensional free
hypermultiplets. Finally, we derive similar statements for three-dimensional
gauge theories such as an SU(2) gauge theory with six chiral doublets or Nf=4
SQED.