Abstract
We study 4d mathcal{N} = 1 gauge theories engineered via D-branes at orientifolds of toric singularities, where gauge anomalies are cancelled without the introduction of non-compact flavor branes. Using dimer model techniques, we derive geometric criteria for establishing whether a given singularity can admit anomaly-free D-brane configurations purely based on its toric data and the type of orientifold projection. Our results therefore extend the dictionary between geometric properties of singularities and physical properties of the corresponding gauge theories.
Highlights
The correspondence between geometry and gauge theory is well understood in the case of 4d N = 1 gauge theories on D3-branes probing toric Calabi-Yau (CY) 3folds, for which the map is significantly streamlined by brane tilings [9, 22, 23]
We generalize the algorithm for solving anomaly cancellation conditions based on zig-zag paths to the case of orientifolds. This analysis will lead to the main result of the paper, which we present in section 5: a purely geometric criterion for anomaly cancellation conditions in orientifold field theories just based on the toric data of the singularity
Geometric algorithm for finding anomaly-free solutions based on zig-zag paths
Summary
ZZPs are in one-to-one correspondence with legs in the (p, q) web diagram [49, 50] (equivalently, the outward pointing vectors normal to the external edges of the toric diagram), where their (p, q) labels are exactly the homology charges of the ZZPs. The ranks Ni of the gauge groups associated to faces in the dimer reflect the configuration of branes at the singularity. The ranks Ni of the gauge groups associated to faces in the dimer reflect the configuration of branes at the singularity These branes include both regular and fractional D3branes. Cancellation of anomalies at a given node of the quiver corresponds to having the same number of incoming and outgoing arrows (weighted by the ranks of the nodes at their other endpoints) This is encoded in the (antisymmetric) matrix A defined as A = A−AT , where Ais the adjacency matrix of the quiver. In this paper we will investigate how these conditions are modified once orientifold planes are introduced
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