Brane boxes, anomalies, bending, and tadpoles

Abstract

Certain classes of chiral four-dimensional gauge theories may be obtained as the world volume theories of D5-branes are 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 an 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 world volume gauge anomaly cancellation. Furthermore, we find additional cylinder amplitudes which give the $\ensuremath{\beta}$ functions of the gauge theory. We show how these correspond to bending of the NS-branes in the brane box theory.