Brane Geometry and Dimer Models
arXiv:1204.1065 · doi:10.1007/JHEP06(2012)143
Abstract
The field content and interactions of almost all known gauge theories in AdS_5/CFT_4 can be expressed in terms of dimer models or bipartite graphs drawn on a torus. Associated with the fundamental cell is a complex structure parameter tau_R. Based on the brane realization of these theories, we can specify a special Lagrangian (SLag) torus fibration that is the natural candidate to be identified as the torus on which the dimer lives. Using the metrics known in the literature, we compute the complex structure tau_G of this torus. For the theories on C^3 and the conifold and for orbifolds thereof tau_R = tau_G. However, for more complicated examples, we show that the two complex structures cannot be equal and yet, remarkably, differ only by a few percent. We leave the explanation for this extraordinary proximity as an open challenge.
29 pages, 4 figures, LaTeX; v.2: references added
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Cited by in corpus (7)
- Gauge Theories and Dessins d'Enfants: Beyond the Torus
- Calabi-Yau Varieties: from Quiver Representations to Dessins d'Enfants
- Consistency and Derangements in Brane Tilings
- Composite Genus One Belyi Maps
- Some Open Questions in Quiver Gauge Theory
- Yang-Mills Theory and the ABC Conjecture
- Metaheuristic Generation of Brane Tilings