Properties of hyperkahler manifolds and their twistor spaces

Abstract

We describe the relation between supersymmetric sigma-models on hyperkahler manifolds, projective superspace, and twistor space. We review the essential aspects and present a coherent picture with a number of new results.

26 pages. v2: Sign mistakes corrected; Kahler potential explicitly calculated in example; references added. v3: Published version--several small clarifications per referee's request

References in corpus (8)

• 4D N = 2 Supergravity and Projective Superspace
• 5D Supergravity and Projective Superspace
• Hyper-Kahler Sigma Models on (Co)tangent Bundles with SO(n) isometry
• Linear perturbations of Hyperkahler metrics
• Polar supermultiplets, Hermitian symmetric spaces and hyperkahler metrics
• Elliptic constructions of hyperkaehler metrics I: The Atiyah-Hitchin manifold
• Elliptic constructions of hyperkaehler metrics II: The quantum mechanics of a Swann bundle
• Elliptic constructions of hyperkaehler metrics III: Gravitons and Poncelet polygons

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• N=2 Conformal Superspace in Four Dimensions
• Twistor Approach to String Compactifications: a Review
• D-instantons and twistors: some exact results
• D3-instantons, Mock Theta Series and Twistors
• Six-dimensional Supergravity and Projective Superfields
• Off-shell superconformal nonlinear sigma-models in three dimensions
• Linear perturbations of quaternionic metrics
• Wall-crossing, Rogers dilogarithm, and the QK/HK correspondence
• On a ${\mathbb{Z}}_2^n$-Graded Version of Supersymmetry
• Lectures on nonlinear sigma-models in projective superspace
• S-duality in Twistor Space
• Some remarks on (super)-conformal Killing-Yano tensors
• 2D N=(4,4) superspace supergravity and bi-projective superfields
• Extended supersymmetric sigma models in AdS_4 from projective superspace
• Goldstino superfields in N=2 supergravity
• A new approach to curved projective superspace
• Supergravity-matter actions in three dimensions and Chern-Simons terms
• N = 2 supersymmetric sigma-models and duality
• Notes on Super Killing Tensors
• On conformal supergravity and harmonic superspace
• An Efficient Representation of Euclidean Gravity I
• On 2D N=(4,4) superspace supergravity
• Hyper-Dilaton Weyl Multiplets of 5D and 6D Minimal Conformal Supergravity
• New extended superconformal sigma models and Quaternion Kahler manifolds
• Relating harmonic and projective descriptions of N=2 nonlinear sigma models
• New Fayet-Iliopoulos terms in $\mathcal{N}=2$ supergravity
• Comments on N = 2 supersymmetric sigma models in projective superspace
• Killing-Yano Cotton Currents
• Heterotic-type II duality in twistor space
• All $(4,0)$: Sigma Models with $(4,0)$ Off-Shell Supersymmetry
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• Fischer Decomposition for osp(4|2)-monogenics in Quaternion Clifford Analysis
• All $(4,1)$: Sigma Models with $(4,q)$ Off-Shell Supersymmetry
• A twistor sphere of generalized Kahler potentials on hyperkahler manifolds
• $\mathcal{N}=2$ super Yang-Mills theory in Projective Superspace
• Darboux Coordinates and Instanton Corrections in Projective Superspace
• Partial $\mathcal{N}=2$ Supersymmetry Breaking and Deformed Hypermultiplets
• Self-dual supersymmetric nonlinear sigma models
• Twisted hyperkähler symmetries and hyperholomorphic line bundles
• Gravitational instantons of type $D_k$ and a generalization of the Gibbons-Hawking Ansatz
• Supersymmetric Sigma Model geometry
• $(0,4)$ Projective Superspaces I: Interacting Linear Sigma Models