N = 2 supersymmetric sigma-models and duality

TL;DR

This paper reformulates N=2 supersymmetric sigma-models in terms of N=1 superfields, revealing their geometric structures and dualities, and presents the most general superconformal model in this framework.

Contribution

It develops a universal N=1 superfield formulation for two classes of N=2 sigma-models and explores their geometric and duality properties, including the explicit superconformal transformations.

Findings

Unified expression for the holomorphic symplectic form ,0

Explicit superconformal transformation formulas

Most general N=2 superconformal sigma-model in N=1 superfields

Abstract

For two families of four-dimensional off-shell N = 2 supersymmetric nonlinear sigma-models constructed originally in projective superspace, we develop their formulation in terms of N = 1 chiral superfields. Specifically, these theories are: (i) sigma-models on cotangent bundles T*M of arbitrary real analytic Kaehler manifolds M; (ii) general superconformal sigma-models described by weight-one polar supermultiplets. Using superspace techniques, we obtain a universal expression for the holomorphic symplectic two-form \omega^{(2,0)} which determines the second supersymmetry transformation and is associated with the two complex structures of the hyperkaehler space T*M that are complimentary to the one induced from M. This two-form is shown to coincide with the canonical holomorphic symplectic structure. In the case (ii), we demonstrate that \omega^{(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 N = 2 supersymmetric nonlinear sigma-models and their on-shell N = 1 chiral realizations. We finally present the most general N = 2 superconformal nonlinear sigma-model formulated in terms of N = 1 chiral superfields. The approach developed can naturally be generalized in order to describe 5D and 6D superconformal nonlinear sigma-models in 4D N = 1 superspace.