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

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arxiv hep-th/0512240 v1 pith:FRP3CDSF submitted 2005-12-19 hep-th

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

classification hep-th
keywords relationsingularitiestoricdiscussgaugeprecisequivertheory
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. $S^3$ partition functions and Equivariant CY$_4 $/CY$_3$ correspondence from Quantum curves

    hep-th 2026-03 conditional novelty 7.0

    Derives Airy representation for S^3 partition functions in M2-brane theories that exactly matches equivariant topological string predictions and proposes a new CY4 to C x CY3 correspondence via quantum curves.

  2. Quiver-Invariant Dualities between Brane Tilings

    hep-th 2026-01 conditional novelty 6.0

    A tilting mutation of brane tilings yields distinct superpotentials on the same quiver with identical mesonic moduli space, equivalent to a sequence of Seiberg dualities.