  We generalize the (p,q) 5-brane web construction of five-dimensional field
theories by introducing (p,q) 7-branes, and apply this construction to theories
with a one-dimensional Coulomb branch. The 7-branes render the exceptional
global symmetry of these theories manifest. Additionally, 7-branes allow the
construction of all E_n theories up to n=8, previously not possible in 5-brane
configurations. The exceptional global symmetry in the field theory is a
subalgebra of an affine symmetry on the 7-branes, which is necessary for the
existence of the system. We explicitly determine the quantum numbers of the BPS
states of all E_n theories using two simple geometrical constraints.
