The Toric Phases of the Y^{p,q} Quivers

TL;DR

The paper addresses the problem of classifying all connected toric phases of the $Y^{p,q}$ quivers and establishing their IR equivalence via Seiberg duality. It introduces an impurity-based construction that starts from the simple $Y^{p,p}$ quiver and, by distributing $p-q$ impurities (single and double), yields all toric phases of $Y^{p,q}$; impurity dynamics under Seiberg duality provide IR equivalence and a picture of their duality network. Using $a$-maximization with the global symmetry $SU(2) imes U(1)_B imes U(1)_F$, it derives the exact $R$-charges for generic toric phases, showing independence from the impurity distribution and matching geometric data of the $Y^{p,q}$ manifolds, including baryonic charges and fractional brane deformations. The work clarifies the toric phase structure of these quivers, highlights the impurity-on-a-circle dynamics as a robust organizational principle, and suggests avenues toward a Diophantine classification and detailed duality cascades in the holographic context.

Abstract

We construct all connected toric phases of the recently discovered $Y^{p,q}$ quivers and show their IR equivalence using Seiberg duality. We also compute the R and global U(1) charges for a generic toric phase of $Y^{p,q}$.

Figures (3)

• Figure 1: Seiberg duality moves the impurities. The notation $S_5$ means Seiberg duality on node 5.
• Figure 2: Single impurities can fuse into double impurities.
• Figure 3: Models with one single and one double impurity and with two double impurities.