Explicit derivation of a new hyper-Kähler metric

Sedra, M. B.

doi:10.1016/s0550-3213(97)00782-7

Cited by 6 publications

(6 citation statements)

References 16 publications

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“…To solve the associated physical equations (20), one may implement auxiliary nodes producing a new quiver with more than two gauge factors. We note that this geometric procedure allows one to modify the above intersection matrix leading to a Calabi-Yau geometry without affecting the dynamical gauge factors.…”

Section: Quiver Gauge Theories From F-theorymentioning

confidence: 99%

“…In fact, these equations look like a generalization of (20). Up to some details, the corresponding physical quantities, like the number of fundamental matter and the gauge group ranks, can be identified with toric data including the Mori vector charges.…”

Section: Quiver Gauge Theories From F-theorymentioning

confidence: 99%

“…Local Calabi-Yau condition (20) requires the introduction of an auxiliary node producing a tetravalent geometry. The latter corresponds to the following Mori vector…”

Section: Quivers From Trivalent Geometrymentioning

confidence: 99%

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F-theory and N = 1 Quivers from Polyvalent Geometry

Belhaj

Sedra

2016

Commun. Theor. Phys.

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We study four dimensional quiver gauge models from F-theory compactified on fourfolds with hyper-Kähler structure. Using intersecting complex toric surfaces, we derive a class of N = 1 quivers with charged fundamental matter placed on external nodes. The emphasis is on how local Calabi-Yau equations solve the corresponding physical constraints including the anomaly cancelation condition. Concretely, a linear chain of SU(N) groups with flavor symmetries has been constructed using polyvalent toric geometry.

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Section: Quiver Gauge Theories From F-theorymentioning

confidence: 99%

Section: Quiver Gauge Theories From F-theorymentioning

confidence: 99%

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F-theory and N = 1 Quivers from Polyvalent Geometry

Belhaj

Sedra

2016

Commun. Theor. Phys.

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“…The idea is based on suggesting new plausible integrable equations by proceeding by formal analogy with the known integrable two dimensional conformal Liouville equation [2,3].…”

Section: Solvable Modelsmentioning

confidence: 99%

A Model for the HyperKahler Metrics Building Program

Boukili¹,

Sedra²,

Zemate³

2012

International Journal of Basic and Applied Sciences

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It's by now well known that the harmonic superspace provides a strong framework for constructing general hyperKähler metrics. Original results in this issue are given by the Taub-Nut and Egushi-Hanson metrics exhibiting both U (1) Pauli-Gursey isomertie as shown by Gibbon et all in [1]. It's also shown that there exist series of potential depending explicitly on the harmonics variables u ± on the sphere S 2 . Based on these knowledge and on previous contributions to the program of metrics building [2, 3], we contribute by presenting a special hyperKähler potential H +4 leading to an α-parametrized Liouville equation on the harmonic superspace. Keywords: Harmonic superspace, HyperKähler metrics, Liouville model, Supersymmetry General SettingThe problem of hyperKähler metrics building is an interesting question of hyperKähler geometry that can be nicely solved in the harmonic superspace (HS) [4,5,2] if one knows how to solve the following nonlinear differential equations on the sphere S 2 :

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“…In section 6, we introduce some pseudo-harmonic differential analysis in order to correctly define the analytic superfields V and V −− as descendants of V ++ . Actually this material is borrowed from the Gelfand-Dickey analysis of 2D integrable Hamiltonian equations systems [13]. In section 7, we give our results and in section 8, we present discussions and give our conclusion.…”

Section: Introductionmentioning

confidence: 99%

On the completely integrable four-dimensional N = 2 hypermultiplet self-couplings

Sahraoui¹,

Saidi²

1999

Class. Quantum Grav.

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Using an adaptation of the Gelfand-Dickey analysis of two-dimensional integrable Hamiltonian systems to the harmonic superspace (HS), we derive a class of completely solvable four-dimensional N = 2 hypermultiplet self-couplings. The known harmonic non-localities are shown to factor out in the HS integrable models. As an illustration, we rederive the Taub-Nut result and obtain a new hyper-Kähler metric associated with a HS superpotential having a pure imaginary coupling constant. A comparison with classes of metrics in the literature is given.

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Explicit derivation of a new hyper-Kähler metric

Abstract: Using the harmonic superspace techniques in D=2 N=4, we present an explicit derivation of a new hyper-Kahler metric associated to the Toda like self interaction H 4+ (ω, u) = ( ξ ++ λ ) 2 exp(2λω). Some important features are also discussed. * mailing address 1

Cited by 6 publications

References 16 publications

F-theory and N = 1 Quivers from Polyvalent Geometry

F-theory and N = 1 Quivers from Polyvalent Geometry

A Model for the HyperKahler Metrics Building Program

On the completely integrable four-dimensional N = 2 hypermultiplet self-couplings

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