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arxiv: hep-th/0512240 · v1 · submitted 2005-12-19 · ✦ hep-th

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From Toric Geometry to Quiver Gauge Theory: the Equivalence of a-maximization and Z-minimization

Agostino Butti , Alberto Zaffaroni
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classification ✦ hep-th
keywords relationsingularitiestoricdiscussgaugeprecisequivertheory
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AdS/CFT predicts a precise relation between the central charge a, the scaling dimensions of some operators in the CFT on D3-branes at conical singularities and the volumes of the horizon and of certain cycles in the supergravity dual. We review how a quantitative check of this relation can be performed for all toric singularities. In addition to the results presented in hep-th/0506232, we also discuss the relation with the recently discovered map between toric singularities and tilings; in particular, we discuss how to find the precise distribution of R-charges in the quiver gauge theory using dimers technology.

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