Brane Boxes, Anomalies, Bending and Tadpoles

TL;DR

The work connects four-dimensional chiral gauge theories realized by brane boxes to string-theoretic consistency: anomaly cancellation is shown to be equivalent to the vanishing of unphysical twisted RR tadpoles in the T-dual orbifold description. By analyzing cylinder amplitudes on a $\mathbb{Z}_k\times\mathbb{Z}_{k'}$ orbifold, the authors relate anomaly constraints to Fourier components of the Chan-Paton data and show that beta-functions arise from partially twisted sectors, interpretable as NS5-brane bending in simple limits. The results provide a precise bridge between worldvolume gauge anomaly freedom and global string consistency, and give a geometric picture of renormalization group flow as brane bending in the brane box setup.

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 $β$-functions of the gauge theory. We show how these correspond to bending of the NS-branes in the brane box theory.

Figures (3)

• Figure 1: One box of a brane box model, showing chiral multiplets.
• Figure 2: Factorization of cylinder, with a twist insertion.
• Figure 3: The corresponding disc amplitudes, appearing in the factorization.