Abstract
Projective superspace provides a natural framework for the construction of actions coupling hypermultiplets to conformal supergravity. We review how the off-shell actions are formulated in superspace and then discuss how to eliminate the infinite number of auxiliary fields to produce an on-shell \( \mathcal{N}=2 \) supersymmetric sigma model, with the target space corresponding to a generic 4n-dimensional hyperkähler cone. We show how the component action coupling the hypermultiplets to conformal supergravity may be constructed starting from curved superspace. The superspace origin of the geometric data — the hyperkähler potential, complex structures, and any gauged isometries — is also addressed.
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ArXiv ePrint: 1410.3604
Dedicated to the memory of Bruno Zumino
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Butter, D. Projective multiplets and hyperkähler cones in conformal supergravity. J. High Energ. Phys. 2015, 161 (2015). https://doi.org/10.1007/JHEP06(2015)161
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DOI: https://doi.org/10.1007/JHEP06(2015)161