Dimer models and toric diagrams

By A. Hanany, Kristian D. Kennaway. 2005

369 citations recorded by the source corpus.

We propose a duality between quiver gauge theories and the combinatorics of dimer models. The connection is via toric diagrams together with multiplicities associated to points in the diagram (which count multiplicities of fields in the linear sigma model construction of the toric space). These multiplicities may be computed from both sides and are found to agree in all known examples. The dimer models provide new insights into the quiver gauge theories: for example they provide a closed formula for the multiplicities of arbitrary orbifolds of a toric space, and allow a new algorithmic method for exploring the phase structure of the quiver gauge theory.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ec70e4f6c410f1989af8580ea1f8956e80411b84

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Citations in the corpus

Brane dimers and quiver gauge theories (2005, methodology): “The connection between dimer models and toric geometry was explored in [24].”
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.”
Brane tilings and their applications (2008, background): “• Since Abelian orbifold of toric Calabi-Yaus corresponds to enlarging the fundamental domain (see Figure 90 for an example), once we know the characteristic polynomial of the parent theory it is easy to compute characteristic polynomial for orbifold theory [25].”
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.”
R-charges from toric diagrams and the equivalence of a-maximization and Z-minimization (2005, methodology): “graph, known as the brane tiling associated with the gauge theory [ 15 ], has F faces,”
Quivers, tilings, branes and rhombi (2005, methodology): “fundamental cell in the brane tiling therefore it justifies the observations made in [ 16 ].”
CONSISTENCY CONDITIONS FOR DIMER MODELS (2011, background): “It was noticed in string theory [11, 8, 10] that under these conditions the algebra A can be described using a dimer model on a torus.”
On the Moduli Space of Elliptic Maxwell-Chern-Simons Theories (2008, neutral): “37 27 v3 [ he p- th ] 1 F eb 2 00 9”
From Sasaki-Einstein spaces to quivers via BPS geodesics: Lp,q|r (2005, methodology): “We have recently witnessed a general progress in the algebro-geometric duality between toric singularities and the gauge theories living on D3 branes probing the singularities: in [28] Hanany and Kennaway put forward a correspondence between the toric data and the corresponding quivers.”
Tilings, Chern-Simons Theories and M2 Branes (2008, methodology): “The periodic tiling of one hexagon is well known to give the N = 4 theory in 3+1 dimensions [4].”
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”
Chiral flavors and M2-branes at toric CY4 singularities (2009, methodology): “In case the CS-matter quiver theory is a brane tiling [53, 54, 55, 49], this branch of the moduli space is a toric CY4.”
Counting BPS operators in gauge theories: quivers, syzygies and plethystics (2006, background): “The dimer for C(3) is well-known [16] and is drawn in Fig.”
Non-commutative Donaldson-Thomas theory and the conifold (2007, background): “rallyby non-commutative geometry and dimer models. Dimers have been in fashion lately in the physics literature, already making an occurence in [22], and independently in work of Hanany and coauthors [14, 11] studying gauge/string duality for toric Calabi–Yau singularities. However, their direct app”