zbMATH — the first resource for mathematics

A note on consistency conditions on dimer models. (English) Zbl 1270.16012
Summary: We show that for a non-degenerate dimer model, both the first consistency condition of S. Mozgovoy and M. Reineke [Adv. Math. 223, No. 5, 1521-1544 (2010; Zbl 1191.14008)] and the properly-orderedness condition of D. R. Gulotta [[J. High Energy Phys. 2008, No. 10, Article ID 014 (2008; Zbl 1245.81091)] are equivalent to a condition on zigzag paths, which goes back to A. Hanany and D. Vegh [J. High Energy Phys. 2007, No. 10, Article ID 029 (2007)]. The last condition is used by the authors [in Dimer models and the special McKay correspondence, arXiv:0905.0059] to study the behavior of a dimer model under the operation of removing a vertex from the lattice polygon and taking the convex hull of the rest.

16G20 Representations of quivers and partially ordered sets
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
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
Full Text: arXiv