Gauge theories from toric geometry and brane tilings

By S. Franco, A. Hanany, D. Martelli, J. Sparks, David Vegh, B. Wecht. 2005

459 citations recorded by the source corpus.

We provide a general set of rules for extracting the data defining a quiver gauge theory from a given toric Calabi-Yau singularity. Our method combines information from the geometry and topology of Sasaki-Einstein manifolds, AdS/CFT, dimers, and brane tilings. We explain how the field content, quantum numbers, and superpotential of a superconformal gauge theory on D3-branes probing a toric Calabi-Yau singularity can be deduced. The infinite family of toric singularities with known horizon Sasaki-Einstein manifolds La,b,c is used to illustrate these ideas. We construct the corresponding quiver gauge theories, which may be fully specified by giving a tiling of the plane by hexagons with certain gluing rules. As checks of this construction, we perform a-maximisation as well as Z-minimisation to compute the exact R-charges of an arbitrary such quiver. We also examine a number of examples in detail, including the infinite subfamily La,b,a, whose smallest member is the Suspended Pinch Point.

Subfields: Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/c998669e6a34b2e69cf1374cacc5361ea4f78bc8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Alberto Zaffaroni
2. A. Hanany
3. J. Sparks
4. D. Martelli
5. F. Benini
6. M. Yamazaki
7. Yang-Hui He
8. S. Franco

In Nuclear and High Energy Physics

1. Alberto Zaffaroni
2. A. Hanany
3. F. Benini
4. D. Martelli
5. J. Sparks
6. Cyril Closset
7. D. Gaiotto
8. N. Seiberg

Citations in the corpus

• Dimer models and the special McKay correspondence (2009, methodology): “A G ] 1 M ay 2 00 9 Dimer models and the special McKay correspondence Akira Ishii and Kazushi Ueda”
• Brane tilings and their applications (2008, unknown): “…. . . . . . . . . 16 2.2 Quiver gauge theories from D3-branes and Calabi-Yau . . . . 18 2.2.1 Orbifold singularities . . . . . . . . . . . . . . . . . . . 18 2.2.2 Toric Calabi-Yau singularities . . . . . . . . . . . . . . 22 2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25”
• Chiral flavors and M2-branes at toric CY4 singularities (2009, background): “A time-filling D3-brane wrapped on the 3-cycle which is the radial section of the toric divisor (such embedding is supersymmetric) corresponds to a dibaryonic operator X η [51, 44, 52].”
• Sasaki–Einstein Manifolds and Volume Minimisation (2006, background): “This has subsequently been generalised to a three–parameter cohomogeneity two family La,b,c [12–14].”
• Supersymmetry on curved spaces and holography (2012, methodology): “In that case we can use the systematic technology of brane tilings [150, 151] extended to M2 branes [152, 153] to compute the volume as a function of the R-charges.”
• N=4 Superconformal Chern-Simons Theories with Hyper and Twisted Hyper Multiplets (2008, unknown): “Contents”
• The Dual superconformal theory for L**pqr manifolds (2005, methodology): “The relation between the total volume and a was recently demonstrated in algebraic way by [21], and the comparison between the geometrical formulae for volumes of divisors and R-charges was done in [ 22 ].”
• THE MASTER SPACE OF N=1 GAUGE THEORIES (2008, background): “Only lately it is realized that the correct way to think about toric geometry in the context of gauge theories is through the language of dimer models and brane tilings [6, 7].”
• Dirichlet Branes and Mirror Symmetry (2009, background): “Let us also mention [151] as a representative work tying together many of the developments we mentioned, along with others such as the relation to dimer models.”
• N=1 theories of class S_k (2015, background): “re are several known large classes of N= 1 superconformal eld theories, which often have some kind of geometric interpretation. A classical example is the class of theories associated to dimer models [1, 2, 3, 4], labelled by bi-partite graphs drawn on a torus and a choice of rank N. These are quive”
• Introduction to Gauge/Gravity Duality (2010, background): “The toric case, where X has a U(1)(3) symmetry, is understood best [55].”
• R-charges from toric diagrams and the equivalence of a-maximization and Z-minimization (2005, background): “The total number of fields is the sum of all the multiplicities: E ≡ ∑ (i,j)∈C |〈vi, vj〉| (3.7) and thus reproduces formula (3.2).”
• Counting BPS operators in gauge theories: quivers, syzygies and plethystics (2006, background): “Currently there are extensive studies of cases with more than one baryonic charge, the simplest being the Suspended Pinch Point (SPP) [9, 18, 34], as well as the more complicated Xp,q family [50].”