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A note on dimer models and McKay quivers. (English) Zbl 1211.81090
Summary: We give one formulation of a procedure of A. Hanany and D. Vegh [Quivers, tilings, branes and rhombi. J. High Energy Phys. 0710, 029, 35 (2007)] which takes a lattice polygon as an input and produces a set of isoradial dimer models. We study the case of lattice triangles in detail and discuss the relation with coamoebas following B. Feng et al. [Adv. Theor. Math. Phys. 12, No. 3, 489–545 (2008; Zbl 1144.81501)].

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
83E30 String and superstring theories in gravitational theory
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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