Hyper-Kähler Metrics Building and Integrable Models

Saidi, E. H.; Sedra, M. B.

doi:10.1142/s0217732394002987

Cited by 14 publications

(17 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…this result is established in [2] and lead to extract important physical and mathematical properties. We derived the following non linear differential equation of motion λ ∂ ++2 ω − ξ ++2 exp 2λω = 0 (16) defining the integrable Liouville field theory.…”

Section: The Hs Liouville Potentialmentioning

confidence: 90%

“…The 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 :…”

Section: General Settingmentioning

confidence: 99%

“…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%

See 2 more Smart Citations

A Model for the HyperKahler Metrics Building Program

Boukili¹,

Sedra²,

Zemate³

2012

International Journal of Basic and Applied Sciences

Self Cite

View full text Add to dashboard Cite

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 :

show abstract

Section: The Hs Liouville Potentialmentioning

confidence: 90%

Section: General Settingmentioning

confidence: 99%

See 1 more Smart Citation

A Model for the HyperKahler Metrics Building Program

Boukili¹,

Sedra²,

Zemate³

2012

International Journal of Basic and Applied Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

“…This linearised equation is remarkably interpreted as the flatness condition of the curvature F +− of two component gauge fields given by A ± . In this gauge language with a Lax pair (A + , A − ) valued in the Lie algebra of ADE, the curvature F +− is given by the commutator [∂ + + A + , ∂ − + A − ] and the flatness condition F +− = 0 leads precisely the above Toda field equations [58,59] recovering the Liouville theory as just the leading r = 1 case. For the case of the geometric engineering of N = 2 supersymmetric QFT 4 's, there is also a classification based on Lie algebras.…”

Section: Qk and Global Isometriesmentioning

confidence: 99%

Partial breaking in the rigid limit of $\mathcal{N}=2$ gauged supergravity

Laamara

Saidi

Vall

2017

Progress of Theoretical and Experimental Physics

View full text Add to dashboard Cite

Using a new manner to rescale fields in N = 2 gauged supergravity with n V vector multiplets and n H hypermultiplets, we develop the explicit derivation of the rigid limit of quaternionic isometry Ward identities agreeing with known results. We show that the rigid limit can be achieved, amongst others, by performing two successive transformations on the covariantly holomorphic sections V M (z,z) of the special Kahler manifold: a particular symplectic change followed by a particular Kahler transformation. We also give a geometric interpretation of the η i parameters used in arXiv:1508.01474 to deal with the expansion of the holomorphic prepotential F (z) of the N = 2 theory. We give as well a D-brane realisation of gauged quaternionic isometries and an interpretation of the embedding tensor ϑ u M in terms of type IIA/IIB mirror symmetry. Moreover, we construct explicit metrics for a new family of 4r-dimensional quaternionic manifolds M (n H ) QK classified by ADE Lie algebras generalising the SO (1, 4) /SO (4) geometry which corresponds to A 1 ∼ su (2). The conditions of the partial breaking of N = 2 supersymmetry in the rigid limit are also derived for both the observable and the hidden sectors. Other features are also studied.

show abstract

“…To solve these equations of motion, one start first by solving the Liouville-like equation of motion Eq. (3.5) whose solution[11], originated from integrability and conformal symmetry in two dimensions, reads in the HS language as[10]…”

mentioning

confidence: 99%