  We present a string theoretical description, given in terms of branes and
orientifolds wrapping vanishing cycles, of the dual pairs of gauge theories
analyzed in 1210.7799. Based on the resulting construction we argue that the
duality that we observe in field theory is inherited from S-duality of type IIB
string theory. We analyze in detail the complex cone over the zeroth del Pezzo
surface and discuss an infinite family of orbifolds of flat space. For the del
Pezzo case we describe the system in terms of large volume objects, and show
that in this language the duality can be understood from the strongly coupled
behavior of the O7^+ plane, which we analyze using simple F-theory
considerations. For all cases we also give a different argument based on the
existence of appropriate torsional components of the 3-form flux lattice. Along
the way we clarify some aspects of the description of orientifolds in the
derived category of coherent sheaves, and in particular we discuss the
important role played by exotic orientifolds - ordinary orientifolds composed
with auto-equivalences of the category - when describing orientifolds of
ordinary quiver gauge theories.
