Polar supermultiplets, Hermitian symmetric spaces and hyperkahler metrics

Abstract

We address the construction of four-dimensional N=2 supersymmetric nonlinear sigma models on tangent bundles of arbitrary Hermitian symmetric spaces starting from projective superspace. Using a systematic way of solving the (infinite number of) auxiliary field equations along with the requirement of supersymmetry, we are able to derive a closed form for the Lagrangian on the tangent bundle and to dualize it to give the hyperkahler potential on the cotangent bundle. As an application, the case of the exceptional symmetric space E_6/SO(10) \times U(1) is explicitly worked out for the first time.

arXiv comment17 pages

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• The CNM-Hypermultiplet Nexus
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Cited by in corpus (17)

• Properties of hyperkahler manifolds and their twistor spaces
• Off-shell superconformal nonlinear sigma-models in three dimensions
• Lectures on nonlinear sigma-models in projective superspace
• The structure of N=2 supersymmetric nonlinear sigma models in AdS_4
• SO and USp Kahler and Hyper-Kahler Quotients and Lumps
• Extended supersymmetric sigma models in AdS_4 from projective superspace
• N = 2 supersymmetric sigma-models and duality
• Chiral formulation for hyperkaehler sigma-models on cotangent bundles of symmetric spaces
• Relating harmonic and projective descriptions of N=2 nonlinear sigma models
• New extended superconformal sigma models and Quaternion Kahler manifolds
• Walls of massive Kähler sigma models on SO(2N)/U(N) and Sp(N)/U(N)
• New supersymmetric sigma-model duality
• Cotangent bundle over Hermitian symmetric space $E_7/E_6\times U(1)$ from projective superspace
• Self-dual supersymmetric nonlinear sigma models
• Walls in supersymmetric massive nonlinear sigma model on complex quadric surface
• Supersymmetry and Cotangent Bundle over Non-compact Exceptional Hermitian Symmetric Space
• Revisiting Atiyah-Hitchin manifold in the generalized Legendre transform