The toric phases of theYp,qquivers

Benvenuti, Sergio; Hanany, Amihay; Kazakopoulos, Pavlos

doi:10.1088/1126-6708/2005/07/021

Cited by 47 publications

(75 citation statements)

References 23 publications

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“…In general N=1 SCFTs, we have to worry about the ambiguity of the field content of the free field approximation due to the Seiberg duality 6 . Even though the entropy in the free Yang-Mills depends on the frame of Seiberg duality or equally on the choice of toric phases of X 5 [24], we will find that this ambiguity changes the entropy only slightly in explicit examples. Thus this does not spoil our semi-quantitative argument in this paper.…”

Section: Entropy From Black Hole and Free Yang-millsmentioning

confidence: 75%

“…Notice that in the above formula (3.1) of the number of matter fields N matter , we are choosing a particular toric phase. We will be able to employ other equivalent descriptions of the quiver gauge theories by applying the Seiberg's duality where the number of matter fields N matter takes different values [24]. As we will see below in the explicit example of Y p,q , this ambiguity changes the value of the ratio f only slightly, though we cannot give a complete general discussion on this issue since its systematic treatment has not been developed well at present.…”

Section: Entropy From Toric Sasaki-einstein Manifoldsmentioning

confidence: 99%

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Free Yang-Mills theory versus toric Sasaki-Einstein manifolds

Nishioka

Takayanagi

2007

Phys. Rev. D

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It has been known that the Bekenstein-Hawking entropy of the black hole in AdS 5 × S 5 agrees with the free N = 4 super Yang-Mills entropy up to the famous factor 4 3 . This factor can be interpreted as the ratio of the entropy of the free Yang-Mills to the entropy of the strongly coupled Yang-Mills. In this paper we compute an analogous factor for infinitely many N = 1 SCFTs which are dual to toric Sasaki-Einstein manifolds. We observed that this ratio always takes values within a narrow range around 4 3 . We also present explicit values of volumes and central charges for new classes of toric Sasaki-Einstein manifolds.

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Section: Entropy From Black Hole and Free Yang-millsmentioning

confidence: 75%

Section: Entropy From Toric Sasaki-einstein Manifoldsmentioning

confidence: 99%

Free Yang-Mills theory versus toric Sasaki-Einstein manifolds

Nishioka

Takayanagi

2007

Phys. Rev. D

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“…It is known that there is a formal similarity between the gauge anomaly cancellation and the baryonic U(1) anomaly cancellation [15,16]. Because of this, we expect that the cancellation of the baryonic U(1) symmetries is also explained by a similar mechanism associated with flux conservation on Σ.…”

Section: Baryonic U(1) Symmetriesmentioning

confidence: 72%

“…toric diagram associated with the Calabi-Yau cone M dual to the brane tiling [15,16]. Furthermore, it is well known that the number of gauge groups, n G , is twice the area of the toric diagram [1,2].…”

Section: Jhep06(2006)011mentioning

confidence: 99%

Anomaly cancellations in brane tilings

Imamura

2006

J. High Energy Phys.

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“…It possesses A symmetry which act on nodes as (1,5,9) (2,6,10) (3,7,11) (4,8,12). The Heisenberg group for this case has been worked out in [2].…”

Section: Center Of the Gauge Groupmentioning

confidence: 99%

Finite Heisenberg groups and Seiberg dualities in quiver gauge theories

et al. 2006

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A large class of quiver gauge theories admits the action of finite Heisenberg groups of the form Heis(Z q × Z q ). This Heisenberg group is generated by a manifest Z q shift symmetry acting on the quiver along with a second Z q rephasing (clock) generator acting on the links of the quiver. Under Seiberg duality, however, the action of the shift generator is no longer manifest, as the dualized node has a different structure from before. Nevertheless, we demonstrate that the Z q shift generator acts naturally on the space of all Seiberg dual phases of a given quiver. We then prove that the space of Seiberg dual theories inherits the action of the original finite Heisenberg group, where now the shift generator Z q is a map among fields belonging to different Seiberg phases. As examples, we explicitly consider the action of the Heisenberg group on Seiberg phases for C 3 /Z 3 , Y 4,2 and Y 6,3 quiver.

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The toric phases of theY^p,qquivers

Abstract: We construct all connected toric phases of the recently discovered Y p,q quivers and show their IR equivalence using Seiberg duality. We also compute the R and global U (1) charges for a generic toric phase of Y p,q .

Cited by 47 publications

References 23 publications

Free Yang-Mills theory versus toric Sasaki-Einstein manifolds

Free Yang-Mills theory versus toric Sasaki-Einstein manifolds

Anomaly cancellations in brane tilings

Finite Heisenberg groups and Seiberg dualities in quiver gauge theories

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