Anomaly Cancellations in Brane Tilings

TL;DR

This work addresses anomaly cancellations in N=1 quiver gauge theories realized by brane tilings by reinterpreting them as flux-conservation conditions on the NS5-brane worldvolume $\Sigma$ via an untwisting map from dimer diagrams. It shows that gauge anomalies correspond to the zero-form flux balance $\sum_a N(a) C_a = 0$, equivalently $\langle C_a, \sum_b N(b) C_b \rangle = 0$, and that baryonic ${\rm U}(1)$ anomalies follow from a similar boundary-condition analysis with wall charges $S(a)$, yielding $\sum_a S(a) C_a = 0$. This establishes a one-to-one link between fractional branes and anomaly-free baryonic symmetries, with the expected count $d-3$, and provides a unified, brane-based mechanism for anomaly cancellation through flux conservation and brane boundary data. The results deepen the geometric and topological understanding of how brane configurations enforce quantum consistency conditions in the corresponding gauge theories.

Abstract

We re-interpret the anomaly cancellation conditions for the gauge symmetries and the baryonic flavor symmetries in quiver gauge theories realized by the brane tilings from the viewpoint of flux conservation on branes.