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The field content and interactions of almost all known gauge theories in AdS5/CFT4 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 τ 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 τ G of this torus. For the theories on ℂ3 and the conifold and for orbifolds thereof τ R = τ 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.
|Uncontrolled Keywords:||Supersymmetry and Duality, D-branes|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||School of Engineering & Mathematical Sciences > Department of Mathematical Science|
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