Comments on Anomalies and Charges of Toric-Quiver Duals

TL;DR

This work establishes a compact geometric formula for triangle 't Hooft anomalies in toric-quiver CFTs dual to toric Sasaki–Einstein manifolds, namely $C_{IJK} = \frac{1}{2} |\langle v_I, v_J, v_K \rangle|$, and uses it to streamline the equivalence of $a$-maximization and $Z$-minimization. It resolves the non-uniqueness of flavor charges by introducing a canonical basis and demonstrates decoupling between baryon and flavor sectors in the $a$-function, connecting field-theory charges to the Reeb-vector data. Through a linearized KK reduction of type IIB supergravity on $\mathrm{AdS}_5\times Y$, it computes the gauge kinetic coefficients $\tau_{IJ}$ and the cubic couplings $C_{IJK}$ on the gravity side and verifies their agreement with field-theory expressions, including the relation $\tau_{IJ} = -3 C_{RIJ}$. The results strengthen the $\mathrm{AdS}_5/\mathrm{CFT}_4$ dictionary for toric-quiver duals and provide explicit, geometry-driven checks of anomaly–current correspondences.

Abstract

We obtain a simple expression for the triangle `t Hooft anomalies in quiver gauge theories that are dual to toric Sasaki-Einstein manifolds. We utilize the result and simplify considerably the proof concerning the equivalence of a-maximization and Z-minimization. We also resolve the ambiguity in defining the flavor charges in quiver gauge theories. We then compare coefficients of the triangle anomalies with coefficients of the current-current correlators and find perfect agreement.

Figures (3)

• Figure 1: Triangle anomaly coefficient as the area of a triangle on the toric diagram.
• Figure 2: The Reeb vector as a point $B$ inside the polygon bz.
• Figure 3: The sign assignment in the second line of (\ref{['qqq']}).