  Certain classes of chiral four-dimensional gauge theories may be obtained as
the worldvolume theories of D5-branes suspended between networks of NS5-branes,
the so-called brane box models. In this paper, we derive the stringy
consistency conditions placed on these models, and show that they are
equivalent to anomaly cancellation of the gauge theories. We derive these
conditions in the orbifold theories which are T-dual to the elliptic brane box
models. Specifically, we show that the expression for tadpoles for unphysical
twisted Ramond-Ramond 4-form fields in the orbifold theory are proportional to
the gauge anomalies of the brane box theory. Thus string consistency is
equivalent to worldvolume gauge anomaly cancellation. Furthermore, we find
additional cylinder amplitudes which give the $\beta$-functions of the gauge
theory. We show how these correspond to bending of the NS-branes in the brane
box theory.
