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Dimer Models from Mirror Symmetry and Quivering Amoebae
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Dimer models are 2-dimensional combinatorial systems that have been shown to encode the gauge groups, matter content and tree-level superpotential of the world-volume quiver gauge theories obtained by placing D3-branes at the tip of a singular toric Calabi-Yau cone. In particular the dimer graph is dual to the quiver graph. However, the string theoretic explanation of this was unclear. In this paper we use mirror symmetry to shed light on this: the dimer models live on a T^2 subspace of the T^3 fiber that is involved in mirror symmetry and is wrapped by D6-branes. These D6-branes are mirror to the D3-branes at the singular point, and geometrically encode the same quiver theory on their world-volume.
Forward citations
Cited by 5 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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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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$Q$-operators, $q$-opers, and R-matrices in 5d $\mathcal{N}=1$ gauge theory
In 5d N=1 U(N) gauge theory, codimension-two defects produce Q-operators whose q-difference equations are the Baxter TQ equations of XXZ spin chains built on bi-infinite evaluation modules of quantum affine algebras.
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Quiver superconformal index and giant gravitons: asymptotics and expansions
For toric quiver theories, coefficients of the large-N superconformal index grow like exp(constant*sqrt(n)) times n^((m-5)/4) for the A-hat_m family, with polynomial growth for dP3 and Y^{p,0}.
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Birational Transformations and 2d (0,2) Quiver Gauge Theories beyond Toric Fano 3-folds
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