New supersymmetric σ-model duality

Abstract

We study dualities in off-shell 4D $ \mathcal{N} = 2 $ supersymmetric σ-models, using the projective superspace approach. These include (i) duality between the real $ \mathcal{O}\left( {2n} \right) $ and polar multiplets; and (ii) polar-polar duality. We demonstrate that the dual of any superconformal σ-model is superconformal. Since $ \mathcal{N} = 2 $ superconformal σ-models (for which target spaces are hyperkähler cones) formulated in terms of polar multiplets are naturally associated with Kähler cones (which are target spaces for $ \mathcal{N} = 1 $ superconformal σ-models), polar-polar duality generates a transformation between different Kähler cones. In the non-superconformal case, we study implications of polar-polar duality for the σ-model formulation in terms of $ \mathcal{N} = 1 $ chiral superfields. In particular, we find the relation between the original hyperkähler potential and its dual. As an application of polar-polar duality, we study self-dual models.