New supersymmetric sigma-model duality

TL;DR

This paper explores dualities in 4D N=2 supersymmetric sigma-models using projective superspace, revealing how dualities relate different geometric structures and extending to superconformal and non-superconformal cases.

Contribution

It introduces new dualities between multiplets in supersymmetric sigma-models and analyzes their implications for target space geometries and superconformal invariance.

Findings

Duality between real O(2n) and polar multiplets.

Polar-polar duality transforms Kahler cones.

Self-dual models are characterized within this duality framework.

Abstract

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