Relating harmonic and projective descriptions of N=2 nonlinear sigma models

Abstract

Recent papers have established the relationship between projective superspace and a complexified version of harmonic superspace. We extend this construction to the case of general nonlinear sigma models in both frameworks. Using an analogy with Hamiltonian mechanics, we demonstrate how the Hamiltonian structure of the harmonic action and the symplectic structure of the projective action naturally arise from a single unifying action on a complexified version of harmonic superspace. This links the harmonic and projective descriptions of hyperkahler target spaces. For the two examples of Taub-NUT and Eguchi-Hanson, we show how to derive the projective superspace solutions from the harmonic superspace solutions.

25 pages; v3: typo fixed in eq (1.36)

References in corpus (5)

• On superconformal projective hypermultiplets
• Hyper-Kahler Sigma Models on (Co)tangent Bundles with SO(n) isometry
• Polar supermultiplets, Hermitian symmetric spaces and hyperkahler metrics
• N = 2 supersymmetric sigma-models and duality
• Chiral formulation for hyperkaehler sigma-models on cotangent bundles of symmetric spaces

Cited by in corpus (6)

• A new approach to curved projective superspace
• On conformal supergravity and harmonic superspace
• $\mathcal{N}=2$ super Yang-Mills theory in Projective Superspace
• Simplifying 4d $\mathcal{N}=3$ Harmonic Superspace
• The Dark Side of Double-Tensor Multiplets
• Five-dimensional non-Abelian supersymmetric Chern-Simons action in Projective Superspace