Brane Boxes, Anomalies, Bending and Tadpoles

TL;DR

This paper establishes a direct link between string consistency conditions and gauge anomaly cancellation in brane box models, also relating brane bending to gauge theory beta-functions.

Contribution

It derives the stringy consistency conditions for brane box models and shows their equivalence to gauge anomaly cancellation, also connecting brane bending to beta-functions.

Findings

String consistency conditions are equivalent to gauge anomaly cancellation.

Tadpole expressions are proportional to gauge anomalies.

Brane bending corresponds to gauge theory beta-functions.

Abstract

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.