R-charges from toric diagrams and the equivalence of a-maximization and Z-minimization

TL;DR

This paper proposes a universal formula for R-charges in gauge theories on toric singularities, demonstrating the equivalence of volume minimization and a-maximization, thus supporting the AdS/CFT correspondence.

Contribution

It introduces a general formula for R-charges and multiplicities, and proves the equivalence of two optimization procedures for all toric diagrams.

Findings

R-charges and multiplicities match toric geometry volumes

Volume minimization and a-maximization are equivalent for all toric diagrams

Supports the validity of AdS/CFT correspondence for toric superconformal theories

Abstract

We conjecture a general formula for assigning R-charges and multiplicities for the chiral fields of all gauge theories living on branes at toric singularities. We check that the central charge and the dimensions of all the chiral fields agree with the information on volumes that can be extracted from toric geometry. We also analytically check the equivalence between the volume minimization procedure discovered in hep-th/0503183 and a-maximization, for the most general toric diagram. Our results can be considered as a very general check of the AdS/CFT correspondence, valid for all superconformal theories associated with toric singularities.