Embedding of theories with<b>SU(2|4)</b>symmetry into the plane wave matrix model

Ishiki, Goro; Shimasaki, Shinji; Takayama, Yastoshi; Tsuchiya, Asato

doi:10.1088/1126-6708/2006/11/089

Cited by 70 publications

(150 citation statements)

References 45 publications

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“…In [15], Takayama and three of the present authors found relationships among the SU(2|4) symmetric theories. Here the SU(2|4) symmetric theories include N = 4 super Yang Mills (SYM) on R × S 3 /Z k , 2+1 SYM on R × S 2 [16] and the plane wave matrix model (PWMM) [17].…”

Section: Introduction and Conclusionsupporting

confidence: 56%

“…Combining these two equivalences, we can say that the theory around each vacuum of N = 4 SYM on R × S 3 /Z k is realized in PWMM. In [15], these equivalences were shown directly on the gauge theory side. The results in [15] not only serve as a nontrivial check of the gauge/gravity correspondence for the SU(2|4) theories, but they are also interesting in the following aspects.…”

Section: Introduction and Conclusionmentioning

confidence: 93%

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Fiber bundles and matrix models

Ishii¹,

Ishiki²,

Shimasaki³

et al. 2008

Phys. Rev. D

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103

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We investigate relationship between a gauge theory on a principal bundle and that on its base space. In the case where the principal bundle is itself a group manifold, we also study relations of those gauge theories with a matrix model obtained by dimensionally reducing them to zero dimensions. First, we develop the dimensional reduction of YangMills (YM) on the total space to YM-higgs on the base space for a general principal bundle. Second, we show a relationship that YM on an SU (2) bundle is equivalent to the theory around a certain background of YM-higgs on its base space. This is an extension of our previous work [29], in which the same relationship concerning a U (1) bundle is shown. We apply these results to the case of SU (n + 1) as the total space. By dimensionally reducing YM on SU (n + 1), we obtain YM-higgs on SU (n + 1)/SU (n) ≃ S 2n+1 and on SU (n + 1)/(SU (n) × U (1)) ≃ CP n and a matrix model. We show that the theory around each monopole vacuum of YM-higgs on CP n is equivalent to the theory around a certain vacuum of the matrix model in the commutative limit. By combining this with the relationship concerning a U (1) bundle, we realize YM-higgs on SU (n + 1)/SU (n) ≃ S 2n+1 in the matrix model. We see that the relationship concerning a U (1) bundle can be interpreted as Buscher's

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Section: Introduction and Conclusionsupporting

confidence: 56%

Section: Introduction and Conclusionmentioning

confidence: 93%

Fiber bundles and matrix models

Ishii¹,

Ishiki²,

Shimasaki³

et al. 2008

Phys. Rev. D

Self Cite

103

View full text Add to dashboard Cite

show abstract

“…The thermodynamics of large N gauge theory on R × S 2 should be also interesting. The relation among these models at zero temperature has been discussed in [6,47,48,8], and it is worth while investigating the relation among their thermodynamics.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…Along the thermal cycle we assign the anti-periodic boundary condition for the fermions. 8 We start from fixing the gauge symmetry and then introduce the Faddeev-Popov determinant conjugate to the gauge fixing. We adopt the Coulomb gauge…”

Section: Path Integral Formulationmentioning

confidence: 99%

“…This metric of S 3 /Z k may be useful since we can easily see that the orbifold action acts on the χ-cycle as χ → χ + 4π/k and that there is no fixed point on this space. The mass of the thermal AdS orbifold is 8) which is 1/k times the mass of the thermal AdS space (4.2). This should be compared with the Casimir energy with the Z k symmetric holonomy.…”

Section: Phase Transitions Of the Orbifoldsmentioning

confidence: 99%

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Phase transitions of largeNorbifold gauge theories

Hikida¹

2006

J. High Energy Phys.

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We study the phase structures of N = 4 U (N ) super Yang-Mills theories on R × S 3 /Z k with large N . The theory has many vacua labelled by the holonomy matrix along the non-trivial cycle on S 3 /Z k , and for the fermions the periodic and the anti-periodic boundary conditions can be assigned along the cycle. We compute the partition functions of the orbifold theories and observe that phase transitions occur even in the zero 't Hooft coupling limit. With the periodic boundary condition, the vacua of the gauge theory are dual to various arrangements of k NS5-branes. With the anti-periodic boundary condition, transitions between the vacua are dual to localized tachyon condensations. In particular, the mass of a deformed geometry is compared with the Casimir energy for the dual vacuum. We also obtain an index for the supersymmetric orbifold theory. *

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Exact results for perturbative partition functions of theories with SU(2|4) symmetry

Asano

Ishiki

Okada

et al. 2013

J. High Energ. Phys.

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In this paper, we study the theories with SU (2|4) symmetry which consist of the plane wave matrix model (PWMM), super Yang-Mills theory (SYM) on R × S 2 and SYM on R × S 3 /Z k . The last two theories can be realized as theories around particular vacua in PWMM, through the commutative limit of fuzzy sphere and Taylor's T-duality. We apply the localization method to PWMM to reduce the partition function and the expectation values of a class of supersymmetric operators to matrix integrals. By taking the commutative limit and performing the T-duality, we also obtain the matrix integrals for SYM on R × S 2 and SYM on R × S 3 /Z k . In this calculation, we ignore possible instanton effects and our matrix integrals describe the perturbative part exactly. In terms of the matrix integrals, we also provide a nonperturbative proof of the large-N reduction for circular Wilson loop operator and free energy in N = 4 SYM on R × S

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Embedding of theories withSU(2|4)symmetry into the plane wave matrix model

Cited by 70 publications

References 45 publications

Fiber bundles and matrix models

Fiber bundles and matrix models

Phase transitions of largeNorbifold gauge theories

Exact results for perturbative partition functions of theories with SU(2|4) symmetry

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