Anomalies and O-plane charges in orientifolded brane tilings

TL;DR

This work develops a consistent framework for orientifolded brane tilings by linking fivebrane systems to toric Calabi–Yau cones. It shows that gauge and Witten anomaly cancellations follow from D5-brane charge conservation, with O5 RR-charges flipping at NS5 intersections necessitating flavor branes that supply the required fundamental fields. It establishes precise mappings between toric data, perfect matchings, zig-zag paths, and mesonic operator parity, tying Z2 parity to RR-charges and enabling a geometric interpretation of quark mass loci that match flavor D7 worldvolumes. Through detailed treatment of minor and major flavor branes and charge-flow mechanisms, the paper provides explicit examples and a robust toolkit for analyzing orientifolded brane tilings, while outlining future directions including O7-planes and dynamical SUSY breaking scenarios.

Abstract

We investigate orientifold of brane tilings. We clarify how the cancellations of gauge anomaly and Witten's anomaly are guaranteed by the conservation of the D5-brane charge. We also discuss the relation between brane tilings and the dual Calabi-Yau cones realized as the moduli spaces of gauge theories. Two types of flavor D5-branes in brane tilings and corresponding superpotentials of fundamental quark fields are proposed, and it is shown that the massless loci of these quarks in the moduli space correctly reproduce the worldvolume of flavor D7-branes in the Calabi-Yau cone dual to the fivebrane system.

Figures (19)

• Figure 1: The bipartite graph of $\mathbb{C}^3$ is shown. This diagram has two vertices of opposite colors, three edges from black to white, and one hexagonal face. Among three arrows representing three adjoint fields and three zig-zag paths representing the boundary of semi-infinite cylinders of NS5-branes, one for each is shown.
• Figure 2: In the O5-plane case, we have four fixed points on $\mathbb{T}^2$. The notation $T= {\genfrac{[}{]}{0pt}{}{{ t_4}\ { t_3}}{{ t_1} \ { t_2}}}$ is meant to represent T-parities of four orientifold planes, as shown in this figure.
• Figure 3: A face with fixed point inside it. The independent bi-fundamental fields are shown as outgoing arrows.
• Figure 4: The D5-brane charges assigned to two adjacent faces and the edge between them are shown.
• Figure 5: The example of the conifold. Here we show $\mathbb{T}^2$ (57) directions. $\mu$, $\nu$, $\rho$, $\sigma$ are cycles of NS5-branes and $a,b,c,d$ are intersection points of O5-planes with D5.

Theorems & Definitions (2)

• Theorem 1
• Theorem 2