From Sasaki-Einstein spaces to quivers via BPS geodesics: Lp,q|r

By S. Benvenuti, M. Kruczenski. 2005

169 citations recorded by the source corpus.

The AdS/CFT correspondence between Sasaki-Einstein spaces and quiver gauge theories is studied from the perspective of massless BPS geodesics. The recently constructed toric Lp,q|r geometries are considered: we determine the dual superconformal quivers and the spectrum of BPS mesons. The conformal anomaly is compared with the volumes of the manifolds. The U(1)2F × U(1)R global symmetry quantum numbers of the mesonic operators are successfully matched with the conserved momenta of the geodesics, providing a test of AdS/CFT duality. The correspondence between BPS mesons and geodesics allows to find new precise relations between the two sides of the duality. In particular the parameters that characterize the geometry are mapped directly to the parameters used for a-maximization in the field theory. The analysis simplifies for the special case of the Lp,q|q models, which are shown to correspond to the known generalized conifolds. These geometries can break conformal invariance through toric deformations of the complex structure.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/af4f65797019fdf922018e1df8afc586b38499eb

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Nuclear and High Energy Physics

1. Alberto Zaffaroni
2. A. Hanany
3. D. Martelli
4. J. Sparks
5. S. Franco
6. S. Benvenuti
7. Yang-Hui He
8. F. Benini

In Statistical and Nonlinear Physics

1. A. Hanany
2. Alberto Zaffaroni
3. Yang-Hui He
4. J. Sparks
5. D. Martelli
6. D. Forcella
7. David Vegh
8. Bo Feng

Citations in the corpus

• Supersymmetry on curved spaces and holography (2012, background): “When these theories can be described as a set of (1, pi) and D3 branes on a circle, they are the extension of the four dimensional L gauge theories [151, 178, 179].”
• Sasaki–Einstein Manifolds and Volume Minimisation (2006, background): “of families of gauge theories that are dual to the wider class of toric Sasaki–Einstein manifolds La,b,c [28,32] (see also [33]).”
• Gauge theories from toric geometry and brane tilings (2005, result): “Note: While this paper was being finalised, we were made aware of other work in [ 49 ], which has some overlap with our results.”
• Counting BPS operators in gauge theories: quivers, syzygies and plethystics (2006, background): “It is recently realised that the toric theories are, in fact, best described using a bi-partite periodic tiling of the two dimensional plane, a so-called “dimer model” [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28] (also cf.”
• R-charges from toric diagrams and the equivalence of a-maximization and Z-minimization (2005, methodology): “of existing results [6, 7 ,9,19] and it is substantially implicit in previous papers on the subject.”
• The Dual superconformal theory for L**pqr manifolds (2005, background): “The relation between the total volume and a was recently demonstrated in algebraic way by [ 21 ], and the comparison between the geometrical formulae for volumes of divisors and R-charges was done in [22].”
• Supersymmetric states of N=4 Yang-Mills from giant gravitons (2006, background): “Over the last few years a number of authors have discovered an infinite number of generalizations of the AdS/CFT conjecture [68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78].”
• Tilings, Chern-Simons Theories and M2 Branes (2008, methodology): “Less ambitiously, it would be interesting to understand if and how we can parametrize R-charges using the toric data of the Calabi-Yau singularity, as it happens in 3+1 dimensions [41, 42, 43, 47].”