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Brane Tilings
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We review and extend the progress made over the past few years in understanding the structure of toric quiver gauge theories; those which are induced on the world-volume of a stack of D3-branes placed at the tip of a toric Calabi-Yau cone, at an ``orbifold point'' in Kaehler moduli space. These provide an infinite class of four-dimensional N=1 superconformal field theories which may be studied in the context of the AdS/CFT correspondence. It is now understood that these gauge theories are completely specified by certain two-dimensional torus graphs, called brane tilings, and the combinatorics of the dimer models on these graphs. In particular, knowledge of the dual Sasaki-Einstein metric is not required to determine the gauge theory, only topological and symplectic properties of the toric Calabi-Yau cone. By analyzing the symmetries of the toric quiver theories we derive the dimer models and use them to construct the moduli space of the theory both classically and semiclassically. Using mirror symmetry the brane tilings are shown to arise in string theory on the world-volumes of the fractional D6-branes that are mirror to the stack of D3-branes at the tip of the cone.
Forward citations
Cited by 6 Pith papers
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Towards Generalized Dimers for GTPs: $\mathcal{N}=2$ Fractional Branes at Infinite Coupling
N=2 strip condensation — collapsing parallel zig-zag strips in brane tilings — reproduces the expected number of gauge groups and yields GTP quivers related to toric ones by relevant deformations.
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The Art of Networking: Networks of Trivalent 10d Heterotic Junctions
The paper constructs arbitrary networks of 10d non-tachyonic heterotic string theories via cobordism-implied junctions and gives worldsheet realizations for graphs, higher-dimensional networks, and compact configurati...
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Abelian Orbifolds for Brane Brick Models
A construction procedure that induces an abelian orbifold action on the fields and J/E-terms of a parent brane brick model for a toric CY4, yielding explicit orbifolded theories that preserve consistency conditions.
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Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues
For quivers satisfying a no-overlap condition, flavored BPS indices are computed by crystal melting derived from Jeffrey-Kirwan residues, and new double quiver algebras are constructed whose crystal representations en...
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On the Origin of Toric Diagrams
A field's scaling dimension equals the number of perfect matchings at the chosen origin that contain it, making the gauge-theory Hilbert series equal the Ehrhart series of the dual polytope.
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Machine Learning Toric Duality in Brane Tilings
Neural networks classify Seiberg dual classes on Z_m x Z_n orbifolds with R^2=0.988 and predict toric multiplicities for Y^{6,0} with mean absolute error 0.021 under fixed Kasteleyn representative.
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