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## A new infinite class of quiver gauge theories (2005)

Venue: | JHEP |

Citations: | 27 - 8 self |

### Citations

5608 | The large N limit of superconformal field theories and supergravity
- Maldacena
- 1998
(Show Context)
Citation Context ...ranes at the tip of a non-compact Calabi-Yau cone; the first such examples of these theories were given for Calabi-Yau spaces which are orbifolds of C3 [1]. More generally, the AdS/CFT correspondence =-=[2, 3, 4]-=- says that there is a gauge/string duality which can be seen by taking the near horizon limit of the D3-branes. The simplest example, where the branes are placed in flat ten dimensional space, gives a... |

2746 |
Gauge theory correlators from non-critical string theory,” Phys. Lett. B428
- Gubser, Klebanov, et al.
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Citation Context ...ranes at the tip of a non-compact Calabi-Yau cone; the first such examples of these theories were given for Calabi-Yau spaces which are orbifolds of C3 [1]. More generally, the AdS/CFT correspondence =-=[2, 3, 4]-=- says that there is a gauge/string duality which can be seen by taking the near horizon limit of the D3-branes. The simplest example, where the branes are placed in flat ten dimensional space, gives a... |

2336 |
Anti-de Sitter space and holography
- Witten
- 1998
(Show Context)
Citation Context ...ranes at the tip of a non-compact Calabi-Yau cone; the first such examples of these theories were given for Calabi-Yau spaces which are orbifolds of C3 [1]. More generally, the AdS/CFT correspondence =-=[2, 3, 4]-=- says that there is a gauge/string duality which can be seen by taking the near horizon limit of the D3-branes. The simplest example, where the branes are placed in flat ten dimensional space, gives a... |

1189 |
Introduction to toric varieties
- Fulton
- 1993
(Show Context)
Citation Context ...striction that the endpoints of these vectors lie in a plane. For this reason, all the toric diagrams we study can be represented on a two-dimensional lattice. For good reviews of toric geometry, see =-=[23, 24, 25]-=-. The construction of quiver gauge theories from toric singularities is a difficult task and many attempts at getting a general formula have been made so far with some or partial success. The – 2 –ge... |

675 | Superconformal field theory on three-branes at a Calabi-Yau singularity, Nucl. Phys. B536
- Klebanov, Witten
- 1998
(Show Context)
Citation Context ...and find that Y p,p = S5 / Z2p, and Y p,0 = T 1,1 / Zp. These spaces are not smooth, but can be used as interesting string backgrounds. The corresponding gauge theories to these spaces are well-known =-=[1, 10, 21, 22]-=-, and the rest of the Y p,q gauge theories were constructed by a simple procedure that generalizes the method for going from Y 2,2 = S 5 / Z2 × Z2 to Y 2,1 = dP1 to Y 2,0 = F0. The fact that the Y p,q... |

329 |
Electric - magnetic duality in supersymmetric nonAbelian gauge theories
- Seiberg
- 1995
(Show Context)
Citation Context .... 5. Toric Phases of the X p,q theories The X p,q quiver gauge theories we present in this paper each flow to a superconformal fixed point at the infrared. At that point one can apply Seiberg duality =-=[36]-=- to any of the gauge groups and get a new theory which has a different matter content and superpotential but flows to the same IR fixed point as the original theory. By repeating this process it is po... |

207 |
Non-spherical horizons
- Morrison, Plesser
- 1999
(Show Context)
Citation Context ...nerally, however, we can place the D3-branes at the tip of a Calabi-Yau cone whose base is a five-dimensional Einstein-Sasaki manifold X5; the near-horizon limit of this is then Type IIB on AdS5 × X5 =-=[5, 6]-=-. This setup breaks additional supersymmetry, generically leaving an N = 1 theory on the D3-branes. These N = 1 theories are quiver gauge theories [1], i.e. theories with product gauge groups and matt... |

175 | D-brane gauge theories from toric singularities and toric duality, Nucl. Phys. B595
- Feng, Hanany, et al.
- 2001
(Show Context)
Citation Context ...,1 was in fact the horizon of the complex cone over the first del Pezzo surface dP1. The corresponding gauge theory is known, having been computed via partial resolution of the orbifold C 3 / Z3 × Z3 =-=[10]-=-. This begged the question: What are the gauge theories dual to the other Y p,q ? The problem of finding these gauge theories was quickly solved. The authors of [11] constructed the dual N = 1 gauge t... |

173 | Toric geometry, Sasaki-Einstein manifolds and a new infinite class of AdS/CFT duals
- Martelli, Sparks
(Show Context)
Citation Context ...actifications of M-theory [8]. The new Einstein-Sasaki spaces have been dubbed Y p,q , where p and q are integers with 0 < q < p; the Calabi-Yau cones over these spaces are toric. Sparks and Martelli =-=[9]-=- recently computed the corresponding toric diagrams and found that Y 2,1 was in fact the horizon of the complex cone over the first del Pezzo surface dP1. The corresponding gauge theory is known, havi... |

153 | The exact superconformal R-symmetry maximizes a,” Nucl. Phys
- Intriligator, Wecht
- 2004
(Show Context)
Citation Context ... symmetries. Similarly, we expect dP2 to have a U(1)×U(1) isometry, which should translate to an additional U(1) 2 flavor symmetry. The baryonic U(1)’s do not mix with the R-symmetry, as discussed in =-=[12, 42]-=-. Therefore there should be a twodimensional space of U(1) symmetries which can potentially mix with the R-symmetry. Indeed, we note that we may assign a 2-dimensional basis of R-charges to the fields... |

146 | Baryons and branes in anti de Sitter space,”
- Witten
- 1998
(Show Context)
Citation Context ...dS/CFT correspondence is that the dimensions of operators in the field theory match with the volumes of the different supersymmetric (calibrated) submanifolds D3– 25 –branes can wrap in the geometry =-=[40, 41]-=-. These dimensions, or equivalently R-charges, can be figured out in the gauge theory via a-maximization, and in the geometry via a volume calculation. These charges have also been computed via techni... |

116 |
New Type IIB Vacua and Their F-Theory Interpretation
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- 1998
(Show Context)
Citation Context ...nerally, however, we can place the D3-branes at the tip of a Calabi-Yau cone whose base is a five-dimensional Einstein-Sasaki manifold X5; the near-horizon limit of this is then Type IIB on AdS5 × X5 =-=[5, 6]-=-. This setup breaks additional supersymmetry, generically leaving an N = 1 theory on the D3-branes. These N = 1 theories are quiver gauge theories [1], i.e. theories with product gauge groups and matt... |

112 | Five-dimensional supersymmetric gauge theories and degenerations of Calabi-Yau spaces,
- Intriligator, Morrison, et al.
- 1997
(Show Context)
Citation Context ...or the 5d theories living on the brane webs dual to the Y p,q toric diagrams with p > 2 we can introduce a Chern-Simons term which turns out to have a coefficent equal to q. As discussed in detail in =-=[35]-=- a massive flavor contributes at the one loop level to the effective Chern-Simons coupling a value of 1/2 and the sign of this contribution is proportional to the sign of the mass of this flavor. As a... |

102 | Toric duality as Seiberg duality and brane diamonds
- Feng, Hanany, et al.
(Show Context)
Citation Context ... This procedure works as expected for the X p,q theories and produces the necessary Y p,q superpotentials upon giving a vev to the appropriate bifundamentals. For more details, we refer the reader to =-=[38, 39]-=-. 6. R-charges An important test of the AdS/CFT correspondence is that the dimensions of operators in the field theory match with the volumes of the different supersymmetric (calibrated) submanifolds ... |

86 |
Supersymmetric AdS5 solutions of M-theory
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- 2004
(Show Context)
Citation Context ...ite family of Einstein-Sasaki manifolds with topology S 2 × S 3 were found by Gauntlett, Sparks, Martelli and Waldram [7]; these extend previous work by these authors on compactifications of M-theory =-=[8]-=-. The new Einstein-Sasaki spaces have been dubbed Y p,q , where p and q are integers with 0 < q < p; the Calabi-Yau cones over these spaces are toric. Sparks and Martelli [9] recently computed the cor... |

79 | superpotentials and superconformal fixed points, Nucl. Phys. B504 - Aharony, Hanany, et al. - 1997 |

78 | Toric duality is Seiberg duality
- Beasley, Plesser
(Show Context)
Citation Context ... This procedure works as expected for the X p,q theories and produces the necessary Y p,q superpotentials upon giving a vev to the appropriate bifundamentals. For more details, we refer the reader to =-=[38, 39]-=-. 6. R-charges An important test of the AdS/CFT correspondence is that the dimensions of operators in the field theory match with the volumes of the different supersymmetric (calibrated) submanifolds ... |

76 | Branes and toric geometry,
- Leung, Vafa
- 1998
(Show Context)
Citation Context ...striction that the endpoints of these vectors lie in a plane. For this reason, all the toric diagrams we study can be represented on a two-dimensional lattice. For good reviews of toric geometry, see =-=[23, 24, 25]-=-. The construction of quiver gauge theories from toric singularities is a difficult task and many attempts at getting a general formula have been made so far with some or partial success. The – 2 –ge... |

72 |
Dimer models and toric diagrams,” arXiv:hep-th/0503149
- Hanany, Kennaway
(Show Context)
Citation Context ...we expect two independent 2-cycles on F0, and since dPn is just IP2 blown up at n points, we expect n + 1 2-cycles for dPn. 1 This rule was discovered empirically with B. Kol; the brane dimer picture =-=[31, 32]-=- provides a proof. – 6 –Figure 3: The toric data for F0 (left), dP1 (center), and dP2 (right). Other (and for our purposes later on, more convenient) toric presentations of these spaces are also poss... |

70 | Phase structure of D-brane gauge theories and toric duality
- Feng, Hanany, et al.
(Show Context)
Citation Context ...and find that Y p,p = S5 / Z2p, and Y p,0 = T 1,1 / Zp. These spaces are not smooth, but can be used as interesting string backgrounds. The corresponding gauge theories to these spaces are well-known =-=[1, 10, 21, 22]-=-, and the rest of the Y p,q gauge theories were constructed by a simple procedure that generalizes the method for going from Y 2,2 = S 5 / Z2 × Z2 to Y 2,1 = dP1 to Y 2,0 = F0. The fact that the Y p,q... |

69 |
New checks and subtleties for AdS/CFT and a-maximization
- Bertolini, Bigazzi, et al.
- 2004
(Show Context)
Citation Context ...lity, such as matching volumes of 3-manifolds in the Calabi-Yau with dimensions of operators in the gauge theory computed via a-maximization [12]. The a-maximization calculation was done for Y 2,1 in =-=[13]-=-, and the authors of [11] found a general formula for the R-charges for any Y p,q ; these agree beautifully with the corresponding volume calculations in the string dual. For interesting related work ... |

59 | Webs of (p,q) 5-branes, five dimensional field theories and grid diagrams, JHEP 01
- Aharony, Hanany, et al.
- 1998
(Show Context)
Citation Context ...striction that the endpoints of these vectors lie in a plane. For this reason, all the toric diagrams we study can be represented on a two-dimensional lattice. For good reviews of toric geometry, see =-=[23, 24, 25]-=-. The construction of quiver gauge theories from toric singularities is a difficult task and many attempts at getting a general formula have been made so far with some or partial success. The – 2 –ge... |

54 | Cascading RG flows from new Sasaki-Einstein manifolds
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- 2005
(Show Context)
Citation Context ...nd a general formula for the R-charges for any Y p,q ; these agree beautifully with the corresponding volume calculations in the string dual. For interesting related work on these Y p,q theories, see =-=[14, 15, 16, 17, 18, 19, 20]-=-. Some of the Y p,q theories and geometries are already familiar. We can formally extend the range of q to 0 ≤ q ≤ p and find that Y p,p = S5 / Z2p, and Y p,0 = T 1,1 / Zp. These spaces are not smooth... |

54 |
Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds.
- Pólya, Read
- 1987
(Show Context)
Citation Context ...hree different colors (corresponding to a single impurity, a double impurity, or no impurity) modulo the action of the dihedral group Dp. This is a standard application of Pólya’s enumeration theorem =-=[37]-=-. The cycle index of the dihedral group – 24 –Y 3,1 14 18 X 3,1 15 17 19 Y 3,0 12 16 Figure 20: The number of fields for the toric phases of X 31 , Y 31 , Y 30 and the possible higgsings (shown with ... |

40 | Small Instantons, Del Pezzo Surfaces and Type I’ Theory, Nucl. Phys. B497
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- 1997
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Citation Context ... p,q theories. The goal of the present paper is to – 3 –generalize this construction. The analogous phenomenon in the context of five dimensional gauge theories with SU(2) gauge group was studied in =-=[25, 26, 29]-=-, where it is associated with a discrete θ angle and the limit of a gauge theory with one flavor that has a large mass. The sign of the mass then implies which of the resulting theories is either F0 o... |

34 |
Dibaryons from exceptional collections
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- 2003
(Show Context)
Citation Context ...lently R-charges, can be figured out in the gauge theory via a-maximization, and in the geometry via a volume calculation. These charges have also been computed via techniques from algebraic geometry =-=[42, 43, 44, 45]-=-. It is also possible to derive some of the R-charges purely from the toric data [30] 7 . Let’s briefly review the situation for dP2, which will reveal an interesting aspect of the Xp,q theories. The ... |

33 | Conformal manifolds for the conifold and other toric field theories, JHEP 0508
- Benvenuti, Hanany
- 2005
(Show Context)
Citation Context ...nd a general formula for the R-charges for any Y p,q ; these agree beautifully with the corresponding volume calculations in the string dual. For interesting related work on these Y p,q theories, see =-=[14, 15, 16, 17, 18, 19, 20]-=-. Some of the Y p,q theories and geometries are already familiar. We can formally extend the range of q to 0 ≤ q ≤ p and find that Y p,p = S5 / Z2p, and Y p,0 = T 1,1 / Zp. These spaces are not smooth... |

33 | Baryon charges in 4D superconformal field theories and their AdS duals,” hep-th/0305046. – 35 – A. Hanany and
- Intriligator, Wecht
- 1999
(Show Context)
Citation Context ...lently R-charges, can be figured out in the gauge theory via a-maximization, and in the geometry via a volume calculation. These charges have also been computed via techniques from algebraic geometry =-=[42, 43, 44, 45]-=-. It is also possible to derive some of the R-charges purely from the toric data [30] 7 . Let’s briefly review the situation for dP2, which will reveal an interesting aspect of the Xp,q theories. The ... |

32 | Multi-flux warped throats and cascading gauge theories
- Franco, Hanany, et al.
- 2005
(Show Context)
Citation Context ...nd a general formula for the R-charges for any Y p,q ; these agree beautifully with the corresponding volume calculations in the string dual. For interesting related work on these Y p,q theories, see =-=[14, 15, 16, 17, 18, 19, 20]-=-. Some of the Y p,q theories and geometries are already familiar. We can formally extend the range of q to 0 ≤ q ≤ p and find that Y p,p = S5 / Z2p, and Y p,0 = T 1,1 / Zp. These spaces are not smooth... |

28 | Exceptional collections and del Pezzo gauge theories
- Herzog
- 2004
(Show Context)
Citation Context ...lently R-charges, can be figured out in the gauge theory via a-maximization, and in the geometry via a volume calculation. These charges have also been computed via techniques from algebraic geometry =-=[42, 43, 44, 45]-=-. It is also possible to derive some of the R-charges purely from the toric data [30] 7 . Let’s briefly review the situation for dP2, which will reveal an interesting aspect of the Xp,q theories. The ... |

23 |
Geometric dualities in 4d field theories and their 5d interpretation, hep-th/0207006; Toric duality, Seiberg duality and Picard-Lefschetz transformations
- Franco, Hanany
(Show Context)
Citation Context ...sional gauge theory living on the 4+1 dimensions common to all the 5-branes. Some things are known about the correspondence between the five dimensional theory and the related four dimensional quiver =-=[34]-=-, but much still remains unkown. Let us now briefly review what is known about (p,q)-webs and the associated 5 dimensional gauge theories. Type IIB string theory has a vast armada of 5+1 dimensional b... |

16 |
geometries and topological string amplitudes, Adv.Theor.Math.Phys
- Iqbal, Kashani-Poor, et al.
(Show Context)
Citation Context ...hich describes the dynamics of a five dimensional SYM SU(p) gauge theory with 8 supercharges, with q denoting the coefficient of a Chern Simons term. Only a few computations have been made since then =-=[27, 28]-=- and many more may be found. Using the connection to five dimensional gauge theories, we are able to borrow ideas from the construction of such theories using branes. In particular the process of addi... |

13 |
The toric phases of the Y(p,q) quivers,” arXiv:hep-th/0412279
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Citation Context |

12 | Unhiggsing the del Pezzo
- Feng, Franco, et al.
- 2003
(Show Context)
Citation Context ...neral idea is to start with a known quiver gauge theory, say Y p,q , blow up its corresponding toric diagram and then to find the effect on the quiver. This procedure was done for several examples in =-=[33]-=-. In many situations there is a unique way to perform such a blow up; this gives the resulting quiver gauge theory. It turns out that in the case we study here we have such a situation in which a blow... |

12 | On correspondences between toric singularities and (p, q)- webs, Nucl. Phys. B701
- Feng, He, et al.
- 2004
(Show Context)
Citation Context ...rge of the bifundamental X56 is given by a root of the polynomial 27x4 − 198x3 − 180x2 + 650x − 250. For X2,2 (also known as Pseudo-del Pezzo 2), the R-charge of one of the fields (X53 in Figure 6 of =-=[46]-=-) is given by a root of 9x4 − 78x3 + 112x2 + 16x + 32. 7. Acknowledgements We would like to thank Alan Dunn, Sebastian Franco, Dan Freedman, Barak Kol, Dario Martelli, and James Sparks for awesome dis... |

10 | Quantum deconstruction of a 5D SYM and its moduli space,” arXiv:hep-th/0212098
- Iqbal, Kaplunovsky
(Show Context)
Citation Context ...hich describes the dynamics of a five dimensional SYM SU(p) gauge theory with 8 supercharges, with q denoting the coefficient of a Chern Simons term. Only a few computations have been made since then =-=[27, 28]-=- and many more may be found. Using the connection to five dimensional gauge theories, we are able to borrow ideas from the construction of such theories using branes. In particular the process of addi... |

10 | Dibaryon spectroscopy
- Herzog, McKernan
- 2003
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3 |
Undoing Orbifold Quivers,” arXiv:hep-th/0502105
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1 |
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