Cones, tri-Sasakian structures and superconformal invariance

Gibbons, G. W.; Rychenkova, P.

doi:10.1016/s0370-2693(98)01287-8

Cited by 65 publications

(100 citation statements)

References 11 publications

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“…In fact, Gibbons and Rychenkova [9] have proven that the characterising property of a metric cone is the existence of a vector field ξ such that∇ ξ V = V for all vector fields V . Let {E i } be a local orthonormal frame for X, and…”

Section: Killing Spinors and Parallel Spinorsmentioning

confidence: 99%

On the supersymmetries of anti-de Sitter vacua

Figueroa-O’Farrill

1999

Class. Quantum Grav.

103

166

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Section: Killing Spinors and Parallel Spinorsmentioning

confidence: 99%

On the supersymmetries of anti-de Sitter vacua

Figueroa-O’Farrill

1999

Class. Quantum Grav.

103

166

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“…Notice that the function F is positive definite in order to have a positive metric. The existence of the homothetic conformal Killing vector allows us to define a new coordinate r = √ 2V , in terms of which the target space metric takes the form of a cone [19] …”

Section: Conformal Sigma Modelsmentioning

confidence: 99%

Superconformal sigma models in three dimensions

Bergshoeff¹,

Cecotti

Samtleben

et al. 2010

Nuclear Physics B

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We construct superconformal gauged sigma models with extended rigid supersymmetry in three dimensions. Those with N > 4 have necessarily flat targets, but the models with N ≤ 4 admit non-flat targets, which are cones with appropriate Sasakian base manifolds. Superconformal symmetry also requires that the three dimensional spacetimes admit conformal Killing spinors which we examine in detail. We present explicit results for the gauged superconformal theories for N = 1, 2. In particular, we gauge a suitable subgroup of the isometry group of the cone in a superconformal way. We finally show how these sigma models can be obtained from Poincaré supergravity. This connection is shown to necessarily involve a subset of the auxiliary fields of supergravity for N ≥ 2.

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“…The obtained metric is a cone [13,10]. To see this, one splits the n + 1 complex variables {X} in {ρ, θ, z α }…”

Section: N = 2 Supergravity and Special Kähler Geometrymentioning

confidence: 99%

Special Kähler Geometry

Proeyen

2001

Quaternionic Structures in Mathematics and Physics

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The geometry that is defined by the scalars in couplings of Einstein-Maxwell theories in N = 2 supergravity in 4 dimensions is denoted as special Kähler geometry. There are several equivalent definitions, the most elegant ones involve the symplectic duality group. The original construction used conformal symmetry, which immediately clarifies the symplectic structure and provides a way to make connections to quaternionic geometry and Sasakian manifolds.

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Cones, tri-Sasakian structures and superconformal invariance

Abstract: In this note we show that rigid N = 2 superconformal hypermultiplets must have target manifolds which are cones over tri-Sasakian metrics. We comment on the relation of this work to cone-branes and the AdS/CFT correspondence.

Cited by 65 publications

References 11 publications

On the supersymmetries of anti-de Sitter vacua

On the supersymmetries of anti-de Sitter vacua

Superconformal sigma models in three dimensions

Special Kähler Geometry

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