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

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

2005-12-19

arxiv.org/abs/hep-th/0512240v1

Fortsch.Phys. 54 (2006) 309-316

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, 4 figures; proceedings of the RTN workshop: ``Constituents, Fundamental Forces and Symmetries of the Universe'', Cor

Scientific paper

10.1002/prop.200510276

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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