An Infinite Family of Superconformal Quiver Gauge Theories with Sasaki-Einstein Duals

TL;DR

The paper constructs an explicit infinite family of four-dimensional N=1 superconformal quiver gauge theories dual to Sasaki–Einstein horizons Y^{p,q}, derived from toric geometry and organized via an iterative quiver-building procedure that starts from Y^{p,p}. By applying a-maximization, the authors obtain exact IR R-charges and show perfect agreement with horizon volumes and baryon charges computed geometrically, establishing a precise gauge/gravity correspondence for the entire Y^{p,q} family. They also analyze global symmetries, dibaryon operators, and Higgsing relations, highlighting a robust link between toric quiver theories and their geometric duals, with implications for higher-dimensional generalizations and M-theory uplifts.

Abstract

We describe an infinite family of quiver gauge theories that are AdS/CFT dual to a corresponding class of explicit horizon Sasaki-Einstein manifolds. The quivers may be obtained from a family of orbifold theories by a simple iterative procedure. A key aspect in their construction relies on the global symmetry which is dual to the isometry of the manifolds. For an arbitrary such quiver we compute the exact R-charges of the fields in the IR by applying a-maximization. The values we obtain are generically quadratic irrational numbers and agree perfectly with the central charges and baryon charges computed from the family of metrics using the AdS/CFT correspondence. These results open the way for a systematic study of the quiver gauge theories and their dual geometries.

Figures (9)

• Figure 1: Triangulation of the toric diagram for $Y^{4,2}$. The number of gauge groups in the associated quiver theory is given by the number of triangles, which in this case is equal to eight.
• Figure 2: Toric diagram and external legs of the corresponding (p,q)-web for $Y^{4,2}$.
• Figure 3: Quiver diagram for the $\hbox{$\,{\rm C}$}^3/{ Z Z}_8$ orbifold. We have color--coded bifundamental fields in accordance to the forthcoming discussion. Superpotential terms appear in the quiver diagram as triangles combining a green, a blue and a cyan arrow.
• Figure 4: Quiver diagram for $Y^{4,3}$, obtained from $Y^{4,4}=\hbox{$\,{\rm C}$}^3/{ Z Z}_8$.
• Figure 5: Quiver diagram for $Y^{4,2}$, obtained from $Y^{4,4}=\hbox{$\,{\rm C}$}^3/{ Z Z}_8$ by applying the three step sequence twice.