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

By Agostino Butti, Alberto Zaffaroni. 2005

156 citations recorded by the source corpus.

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.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/d43957a0887e1002810c64ae3b0d7b12763569cf

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In Nuclear and High Energy Physics

Citations in the corpus

F-theorem without supersymmetry (2011, unknown): “This equivalence was proved in [9, 10].”
Maximally homogeneous para-CR manifolds of semisimple type (2006, unknown): “They created an avalanche of papers studying the properties of these metrics from the physics perspective [ABCC06, OY06c, OY06b, OY06a, KSY05, HEK05, BZ05 , BBC05, BFZ05, SZ05, HKW05, BLMPZ05, BHK05, BFH + 05, Pal05, HSY04].”
Supersymmetry on curved spaces and holography (2012, methodology): “The analogue fact for a in four dimensions has been shown to be generally true [20, 21], in three dimensions so far this holds only at the level of observation.”
Brane tilings and their applications (2008, background): “motivated an upsurge of interest in this field, culminating for example in the construction of gauge theory duals of Y p,q and L Sasaki-Einstein manifolds [26–28] and in the proof [33,34] of the equivalence of a-maximization [35] and Z-minimization [36, 37] (see §5).”
Supersymmetric AdS5 solutions of type IIB supergravity (2005, background): “It would be also very interesting to see if there is a generalisation of Zminimisation [39] (see also [ 40 , 41, 42]), a geometrical version of a-maximisation [43] in the toric Sasaki–Einstein setting, to the more general class of geometries analysed here.”
Counting BPS operators in gauge theories: quivers, syzygies and plethystics (2006, unknown): “so-called “dimer model” [16, 17, 18, 19, 20 , 21, 22, 23, 24, 25, 26, 27, 28] (also cf. [29, 30]”
Sasaki–Einstein Manifolds and Volume Minimisation (2006, methodology): “An analytic proof of the equivalence of these two optimisation problems was given in the work of [29], modulo certain assumptions on the matter content of the field theory.”
THE MASTER SPACE OF N=1 GAUGE THEORIES (2008, background): “35) that this prescription is equivalent to the one discussed in [28, 29].”
Towards the F-theorem: $ \mathcal{N} = 2 $ field theories on the three-sphere (2011, methodology): “A similar relation in the case of (3 + 1)-dimensional gauge theories between Z and the anomaly coefficient a was found in [23].”
Tilings, Chern-Simons Theories and M2 Branes (2008, background): “This comparison can be done for a generic toric three-fold [44] and it is a highly non-trivial check of the correspondence between Tilings and toric Calabi-Yau singularities.”