Stationary Riemannian space-times with self-dual curvature

Gegenberg, J.; Das, A.

doi:10.1007/bf00762935

Cited by 85 publications

(67 citation statements)

References 13 publications

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“…where a 1 (x, y, z) is the value of A at t = 0 as in (20). The exponential here is defined by its power series with the n'th term in this series being…”

Section: Construction Of Self-duality Conditionmentioning

confidence: 99%

On self-dual gravity

Grant

1993

Phys. Rev. D

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We study the Ashtekar-Jacobson-Smolin equations that characterise four dimensional complex metrics with self-dual Riemann tensor.We find that we can characterise any self-dual metric by a function that satisfies a non-linear evolution equation, to which the general solution can be found iteratively. This formal solution depends on two arbitrary functions of three coordinates. We construct explicitly some families of solutions that depend on two free functions of two coordinates, included in which are the multi-centre metrics of Gibbons and Hawking.

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“…where a 1 (x, y, z) is the value of A at t = 0 as in (20). The exponential here is defined by its power series with the n'th term in this series being…”

Section: Construction Of Self-duality Conditionmentioning

confidence: 99%

On self-dual gravity

Grant

1993

Phys. Rev. D

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“…which is the Toda frame [16][17][18]. For this metric the self-duality (or anti-self duality) condition is the three-dimensional continual Toda (1.4) which here we write using complex coordinates 2q = x + iy and c.c.…”

Section: Jhep11(2013)118mentioning

confidence: 99%

Gravity duals of $ \mathcal{N} $ = 2 superconformal field theories with no electrostatic description

Petropoulos

Sfetsos

Σιάμπος

2013

J. High Energ. Phys.

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Abstract:We construct the first eleven-dimensional supergravity solutions, which are regular, have no smearing and possess only SO(2, 4) × SO(3) × U(1) R isometry. They are dual to four-dimensional field theories with N = 2 superconformal symmetry. We utilise the Toda frame of self-dual four-dimensional Euclidean metrics with SU(2) rotational symmetry. They are obtained by transforming the Atiyah-Hitchin instanton under SL(2, R) and are expressed in terms of theta functions. The absence of any extra U(1) symmetry, even asymptotically, renders inapplicable the electrostatic description of our solution.

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“…Consequently, in hyper-Kähler spaces, a Killing vector is translational if k − uv = 0, and rotational otherwise [17][18][19][20]. In order to clarify the meaning of translational versus rotational isometry, we evaluate the Lie derivative on the complex structures with respect to the Killing vector ξ: …”

Section: Jhep11(2016)169mentioning

confidence: 99%

“…The scalar potential (5.12) becomes 19) in the rigid limit (5.7), with g = − g 2(kμ) 4/3 a finite coupling constant at k → 0. Again, the cosmological constant vanishes and we describe a global N = 2 hypermultiplet in Minkowski spacetime.…”

Section: The Scalar Potentialmentioning

confidence: 99%

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Isometries, gaugings and N $$ \mathcal{N} $$ = 2 supergravity decoupling

Antoniadis

Derendinger

Petropoulos

et al. 2016

J. High Energ. Phys.

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We study off-shell rigid limits for the kinetic and scalar-potential terms of a single N = 2 hypermultiplet. In the kinetic term, these rigid limits establish relations between four-dimensional quaternion-Kähler and hyper-Kähler target spaces with symmetry. The scalar potential is obtained by gauging the graviphoton along an isometry of the quaternion-Kähler space. The rigid limits unveil two distinct cases. A rigid N = 2 theory on Minkowski or on AdS 4 spacetime, depending on whether the isometry is translational or rotational respectively. We apply these results to the quaternion-Kähler space with Heisenberg ⋉ U(1) isometry, which describes the universal hypermultiplet at type-II string one-loop.

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Stationary Riemannian space-times with self-dual curvature

Cited by 85 publications

References 13 publications

On self-dual gravity

On self-dual gravity

Gravity duals of $ \mathcal{N} $ = 2 superconformal field theories with no electrostatic description

Isometries, gaugings and N $$ \mathcal{N} $$ = 2 supergravity decoupling

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