Journal of High Energy Physics

, 2010:115 | Cite as

\( \mathcal{N} = 2 \) supersymmetric sigma-models and duality

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Abstract

For two families of four-dimensional off-shell \( \mathcal{N} = 2 \) supersymmetric nonlinear σ-models constructed originally in projective superspace, we develop their formulation in terms of \( \mathcal{N} = 1 \) chiral superfields. Specifically, these theories are:
  1. (i)

    σ-models on cotangent bundles \( T^{*}\mathcal{M} \) of arbitrary real analytic Kähler manifolds \( \mathcal{M} \);

     
  2. (ii)

    general superconformal σ-models described by weight-one polar supermultiplets.

     

Using superspace techniques, we obtain a universal expression for the holomorphic symplectic two-form ω (2,0) which determines the second supersymmetry transformation and is associated with the two complex structures of the hyperkähler space \( T^{*}\mathcal{M} \) that are complimentary to the one induced from \( \mathcal{M} \). This two-form is shown to coincide with the canonical holomorphic symplectic structure. In the case (ii), we demonstrate that ω (2,0) and the homothetic conformal Killing vector determine the explicit form of the superconformal transformations. At the heart of our construction is the duality (generalized Legendre transform) between off-shell \( \mathcal{N} = 2 \) supersymmetric nonlinear σ-models and their on-shell \( \mathcal{N} = 1 \) chiral realizations. We finally present the most general \( \mathcal{N} = 2 \) superconformal nonlinear σ-model formulated in terms of \( \mathcal{N} = 1 \) chiral superfields. The approach developed can naturally be generalized in order to describe 5D and 6D superconformal nonlinear σ-models in 4D \( \mathcal{N} = 1 \) superspace.

Keywords

Supersymmetry and Duality Extended Supersymmetry Superspaces Supersymmetric Effective Theories 
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Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

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

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