Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A New Infinite Class of Quiver Gauge Theories

Amihay Hanany, Pavlos Kazakopoulos, Brian Wecht

TL;DR

The authors introduce an infinite family of ${X^{p,q}}$ quiver gauge theories that Higgs to the ${Y^{p,q}}$ class, providing toric data for the dual Calabi–Yau cones and exploring Seiberg dual toric phases. They connect these 4d theories to $(p,q)$ 5-brane webs and discuss the limitations in determining the Sasaki–Einstein metrics, while showing that R-charges are generally algebraic and not restricted to quadratic irrationals. The construction extends the landscape of AdS/CFT duals by bridging toric geometry, Higgsing, and 5d gauge theory dynamics, and highlights rich structures in toric phases and R-charge manifolds. Overall, the work broadens the catalog of quiver gauge theories with explicit toric data and deepens the interplay between geometry, dualities, and higher-dimensional brane constructions.

Abstract

We construct a new infinite family of N=1 quiver gauge theories which can be Higgsed to the Y^{p,q} quiver gauge theories. The dual geometries are toric Calabi-Yau cones for which we give the toric data. We also discuss the action of Seiberg duality on these quivers, and explore the different Seiberg dual theories. We describe the relationship of these theories to five dimensional gauge theories on (p,q) 5-branes. Using the toric data, we specify some of the properties of the corresponding dual Sasaki-Einstein manifolds. These theories generically have algebraic R-charges which are not quadratic irrational numbers. The metrics for these manifolds still remain unknown.

A New Infinite Class of Quiver Gauge Theories

TL;DR

The authors introduce an infinite family of quiver gauge theories that Higgs to the class, providing toric data for the dual Calabi–Yau cones and exploring Seiberg dual toric phases. They connect these 4d theories to 5-brane webs and discuss the limitations in determining the Sasaki–Einstein metrics, while showing that R-charges are generally algebraic and not restricted to quadratic irrationals. The construction extends the landscape of AdS/CFT duals by bridging toric geometry, Higgsing, and 5d gauge theory dynamics, and highlights rich structures in toric phases and R-charge manifolds. Overall, the work broadens the catalog of quiver gauge theories with explicit toric data and deepens the interplay between geometry, dualities, and higher-dimensional brane constructions.

Abstract

We construct a new infinite family of N=1 quiver gauge theories which can be Higgsed to the Y^{p,q} quiver gauge theories. The dual geometries are toric Calabi-Yau cones for which we give the toric data. We also discuss the action of Seiberg duality on these quivers, and explore the different Seiberg dual theories. We describe the relationship of these theories to five dimensional gauge theories on (p,q) 5-branes. Using the toric data, we specify some of the properties of the corresponding dual Sasaki-Einstein manifolds. These theories generically have algebraic R-charges which are not quadratic irrational numbers. The metrics for these manifolds still remain unknown.

Paper Structure

This paper contains 12 sections, 17 equations, 20 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Warm-Ups: del Pezzo 2 and the Suspended Pinch Point
  3. New quiver theories: $X^{p,q}$
  4. Review of the $Y^{p,q}$ quivers
  5. $X^{p,q}$ for $1 \leq q \leq p-1$
  6. $X^{p,q}$ for $q=p$
  7. An example: $X^{3,1}$, $X^{3,2}$, and $X^{3,3}$
  8. Toric Diagrams for $X^{p,q}$
  9. (p,q)-brane webs and 5d gauge theories
  10. Toric Phases of the $X^{p,q}$ theories
  11. R-charges
  12. Acknowledgements

Figures (20)

  • Figure 1: One quiver for the $dP_2$ gauge theory.
  • Figure 2: The quivers for $Y^{2,1}$ (left) and $Y^{2,0}$ (right)
  • Figure 3: The toric data for $\hbox{$\,{\rm F}$}_0$ (left), $dP_1$ (center), and $dP_2$ (right).
  • Figure 4: Alternate toric data for $\hbox{$\,{\rm F}$}_0$ (left) $dP_1$ (center), and $dP_2$ (right).
  • Figure 5: The SPP quiver (top) can be Higgsed to the conifold (bottom left) or the $\hbox{$\,{\rm C}$}^3/{ Z Z}_2$ theory (bottom right).
  • ...and 15 more figures