  We study gauge theories on the world-volume of D3-branes probing
singularities. Seiberg duality can be realized as a sequence of
Picard-Lefschetz monodromies on 3-cycles in the mirror manifold. In previous
work, the precise meaning of gauge theories obtained by monodromies that do not
correspond to Seiberg duality was unclear. Recently, it was pointed out that
these theories contain tachyons, suggesting that the collection of marginally
bound branes at the singularity is unstable. We address this problem using
(p,q) web techniques. It is shown that theories with tachyons appear whenever
the (p,q) web contains crossing legs. A recent study of these theories with
tachyons using exceptional collections proposed the notion of "well split
condition.'' We show the equivalence between the well split condition and the
absence of crossing legs in the (p,q) web. The (p,q) web has a natural
resolution of crossing legs which was first studied in the construction of five
dimensional fixed points using branes. Exploiting this result, we propose a
generic procedure which determines the quiver that corresponds to the stable
bound state of D-branes that live on the singularity after the monodromy. This
set is generically larger than the original set, meaning that there are extra
massless gauge fields and matter fields in the quiver. Alternatively, one can
argue that since these gauge and matter fields are initially assumed to be
absent, the theory exhibits tachyonic excitations. We illustrate our ideas in
an explicit example for D3-branes on a complex cone over dP1, computing both
the quiver and the superpotential.
