New checks and subtleties for AdS/CFT and a-maximization

By M. Bertolini, F. Bigazzi, A. Cotrone. 2004

153 citations recorded by the source corpus.

We provide a cross-check of AdS/CFT and a-charge maximization for a four dimensional = 1 SCFT with irrational R-charges. The gauge theory is the low energy effective theory of N D3-branes at the tip of the complex cone over the first del Pezzo surface. By carefully taking into account the subtle issue of flavor symmetry breaking at the fixed point, we show, using a-maximization, that this theory has in fact irrational central charge and R-charges. Our results perfectly match with those inherited from the recently discovered supergravity dual background. Along analogous lines, we make novel predictions for the still unknown AdS dual of the quiver theory for the second del Pezzo surface. This should flow to a SCFT with irrational charges, too. All of our results differ from previous findings in the literature and outline interesting subtleties in a-maximization and AdS/CFT techniques overlooked in the past.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/e07808a64a2131daa85de615dc8a04edc89f4b15

How researchers see this paper

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

In Astronomy and Astrophysics

1. D. Martelli
2. J. Sparks
3. J. Gauntlett
4. D. Waldram
5. Alberto Zaffaroni
6. A. Hanany
7. Shing-Tung Yau
8. S. Franco

In Nuclear and High Energy Physics

1. Alberto Zaffaroni
2. J. Sparks
3. D. Martelli
4. A. Hanany
5. M. Yamazaki
6. S. Franco
7. J. Gauntlett
8. S. Benvenuti

Citations in the corpus

• Supersymmetric AdS5 solutions of type IIB supergravity (2005, background): “ [6, 9], respectively. The solutions found in [2] led to an infinite number of new explicit Sasaki–Einstein metrics on S2 ×S3 called Yp,q [10]. The dual conformal field theories have now been identified [12, 13, 14] and there have been many further checks and developments. The Yp,q metrics were general”
• Brane tilings and their applications (2008, background): “In fact, historically this was first derived from the field theory computation in the pioneering work of [153].”
• An Infinite Family of Superconformal Quiver Gauge Theories with Sasaki-Einstein Duals (2004, result): “The gauge theory for this geometry is presented in [21], and has been discussed in [26] which resolved an apparent puzzle for this case, reconciling the gauge theory results with the geometric analysis of [14].”
• Dynamical SUSY breaking at meta-stable minima from D-branes at obstructed geometries (2006, background): “The resulting quiver gauge theories lead, in the absence of fractional branes, to a tractable class of 4d strongly coupled conformal field theories, which extend the AdS/CFT correspondence [1 – 3] to theories with reduced (super)symmetry [4 – 6] and enable non-trivial precision tests of the correspo”
• Tilings, Chern-Simons Theories and M2 Branes (2008, result): “In the 3+1 dimensional case, we can explicitly compare the results of a-maximization [37, 38] with the spectrum of dimensions computed from volumes of cycles in H and gain confidence in our identification of the quiver gauge theory as the dual of AdS4×H [39, 40, 41, 42, 43].”
• Brane dimers and quiver gauge theories (2005, methodology): “ been known. One of the simplest examples is Y2,1, which turns out to be the SE manifold which is the base of the complex cone over the first del Pezzo surface. The R-charges for Y2,1 were computed in [23] and shown to agree exactly with the geometrical computation done using the metric found in [22]”
• Transverse Kähler geometry of Sasaki manifolds and toric Sasaki-Einstein manifolds (2006, methodology): “The irregularity of the example mentioned in Corollary 1.3 follows from the computations given by Martelli, Sparks and Yau [33]; there is an earlier computation by Bertolini, Bigazzi and Cotrone for the dual theory through AdS/CFT correspondence [4].”
• Supersymmetry Breaking from a Calabi-Yau Singularity (2005, background): “J H E P 0 9 ( 2 0 0 5 ) 0 8 4 expectations [9, 12, 13].”
• The Geometric Dual of a–Maximisation for Toric Sasaki–Einstein Manifolds (2005, methodology): “It is then straightforward to match these with the R–charges of fields computed in reference [21].”
• Toric Geometry, Sasaki–Einstein Manifolds and a New Infinite Class of AdS/CFT Duals (2004, methodology): “In particular we may compare our geometrical results to the a-maximisation calculation20 presented in [14].”
• Gauge theories from toric geometry and brane tilings (2005, unknown): “For example, remarkable agreement was found for these two computations in the case of the Y p,q singularities [45, 13].”
• Fractional branes and dynamical supersymmetry breaking (2005, background): “7.1 Brane tiling perspective of fractional branes 30 7.2 Beta function relations and baryonic U(1) symmetries from brane tilings 35”
• Sasaki–Einstein Manifolds and Volume Minimisation (2006, background): “Indeed, remarkable agreement was found between the geometrical computation in the case of the Y p,q metrics [10,23] and the a–maximisation calculation [24,25] for the corresponding quiver gauge theories.”