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Relating harmonic and projective descriptions of N=2 nonlinear sigma models
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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.
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On three-dimensional ${\cal N}=4$ supersymmetry: maximally supersymmetric backgrounds and massive deformations
The paper classifies maximally supersymmetric 3D N=4 backgrounds and constructs massive deformations of N=4 theories on deformed Minkowski superspace, including a one-loop derivation of Chern-Simons terms.
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