Brane dimers and quiver gauge theories

By S. Franco, A. Hanany, Kristian D. Kennaway, David Vegh, B. Wecht. 2005

536 citations recorded by the source corpus.

We describe a technique which enables one to quickly compute an infinite number of toric geometries and their dual quiver gauge theories. The central object in this construction is a ``brane tiling,'' which is a collection of D5-branes ending on an NS5-brane wrapping a holomorphic curve that can be represented as a periodic tiling of the plane. This construction solves the longstanding problem of computing superpotentials for D-branes probing a singular non-compact toric Calabi-Yau manifold, and overcomes many difficulties which were encountered in previous work. The brane tilings give the largest class of = 1 quiver gauge theories yet studied. A central feature of this work is the relation of these tilings to dimer constructions previously studied in a variety of contexts. We do many examples of computations with dimers, which give new results as well as confirm previous computations. Using our methods we explicitly derive the moduli space of the entire Yp,q family of quiver theories, verifying that they correspond to the appropriate geometries. Our results may be interpreted as a generalization of the McKay correspondence to non-compact 3-dimensional toric Calabi-Yau manifolds.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/71798f25f17b50ad36a1a95805577ac8be12ab5b

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 Mathematical Physics

1. Alberto Zaffaroni
2. F. Benini
3. A. Hanany
4. D. Martelli
5. A. Tomasiello
6. D. Gaiotto
7. Yinan Song
8. C. Vafa

In Nuclear and High Energy Physics

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

Citations in the corpus

• R-charges from toric diagrams and the equivalence of a-maximization and Z-minimization (2005, methodology): “In [15] it was suggested a natural one to one correspondence between auxiliary fields in the Witten sigma model associated to a quiver theory and perfect matchings of the dimer configuration.”
• 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”
• Tilings, Chern-Simons Theories and M2 Branes (2008, methodology): “After adding a diagonal on this hexagon [5], the resulting tiling corresponds to C, the conifold theory, a quiver with two gauge groups, fields Ai, Bi, i = 1, 2 transforming in the (N, N̄) and (N̄ , N) representation of the gauge group, respectively, and interacting with the superpotential W = A1B1A”
• Counting BPS operators in gauge theories: quivers, syzygies and plethystics (2006, background): “Being toric, this CY manifold admits a description in terms of periodic bi-partite tilings of the two dimensional plane and in fact is given by the simplest of them all - tilings by regular hexagons [17].”
• Dimer models and toric diagrams (2005, background): “Dimer models 5 3.1 Examples 8 3.2 Orbifolds 10”
• N=1 theories of class S_k (2015, background): “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 .”
• A simple class of N = 3 gauge/gravity duals (2008, background): “The field theories can be engineered from a brane configuration; their geometry is summarized by a “hyperKähler toric fan” that can be read off easily from the relative angles of the branes.”
• Gauge theories from toric geometry and brane tilings (2005, methodology): “The initial connection between toric geometry and dimers was suggested in [47]; the connection to N = 1 theories was proposed and explored in [48].”
• A theory of generalized Donaldson–Thomas invariants (2008, background): “This class of examples arose in String Theory, where they are known as ‘quiver gauge theories’ or ‘dimer models’, and appear in the work of Hanany and others, see for instance [26, 36–38].”
• Dimer models and cluster categories of Grassmannians (2013, background): “From the construction, Q(D) may be embedded in the disk in which D is drawn and it is natural to interpret it as a dimer model with boundary, as a generalisation of dimer models on a torus or a more general closed surface (see [2], [3], [7], [12]).”
• N=4 Superconformal Chern-Simons Theories with Hyper and Twisted Hyper Multiplets (2008, unknown): “Contents”