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Journal of High Energy Physics

, 2011:80 | Cite as

The structure of \( \mathcal{N} = {2} \) supersymmetric nonlinear sigma models in AdS4

  • Daniel Butter
  • Sergei M. Kuzenko
Article

Abstract

We present a detailed study of the most general \( \mathcal{N} = {2} \) supersymmetric sigma models in four-dimensional anti-de Sitter space (AdS4) formulated in terms of \( \mathcal{N} = 1 \) chiral superfields. The target space is demonstrated to be a non-compact hyperkähler manifold restricted to possess a special Killing vector field which generates an SO(2) group of rotations on the two-sphere of complex structures and necessarily leaves one of them invariant. All hyperkähler cones, that is the target spaces of \( \mathcal{N} = {2} \) superconformal sigma models, prove to possess such a vector field that belongs to the Lie algebra of an isometry group SU(2) acting by rotations on the complex structures. A unique property of the \( \mathcal{N} = {2} \) sigmamodelsconstructedisthatthealgebraofOSp(2|4)transformationsclosesoff the mass shell. We uncover the underlying \( \mathcal{N} = {2} \) superfield formulation for the \( \mathcal{N} = {2} \) sigma models constructed and compute the associated \( \mathcal{N} = {2} \) supercurrent. We give a special analysis of the most general systems of self-interacting \( \mathcal{N} = {2} \) tensor multiplets in AdS4 and their dual sigma models realized in terms of \( \mathcal{N} = 1 \) chiral multiplets. We also briefly discuss the relationship between our results on \( \mathcal{N} = {2} \) supersymmetric sigma models formulated in the \( \mathcal{N} = 1 \) AdS superspace and the off-shell sigma models constructed in the \( \mathcal{N} = {2} \) AdS superspace in arXiv:0807.3368.

Keywords

Supersymmetry and Duality Extended Supersymmetry Superspaces Supersymmetric Effective Theories 

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© SISSA, Trieste, Italy 2011

Authors and Affiliations

  1. 1.School of Physics M013The University of Western AustraliaCrawleyAustralia

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