On superpotentials for nonlinear sigma-models with eight supercharges

TL;DR

This paper explores how superpotentials can be generated in 4D N=2 and 5D N=1 gauged supersymmetric nonlinear sigma-models with hyper-Kahler target spaces, using projective superspace techniques and gauge fixing.

Contribution

It demonstrates the generation of chiral superpotentials via gauging holomorphic isometries and freezing background multiplets, linking to recent results in supersymmetric theories.

Findings

Superpotentials arise from gauging isometries and fixing background multiplets.

The approach connects 4D N=2 superspace techniques with recent superpotential results.

The analysis clarifies the superspace origin of these superpotentials.

Abstract

Using projective superspace techniques, we consider 4D N = 2 and 5D N = 1 gauged supersymmetric nonlinear sigma-models for which the hyper-Kahler target space is (an open domain of the zero section of) the cotangent bundle of a real-analytic Kahler manifold. As in the 4D N = 1 case, one may gauge those holomorphic isometries of the base Kahler manifold (more precisely, their lifting to the cotangent bundle) which are generated by globally defined Killing potentials. In the U(1) case, by freezing the background vector (tropical) multiplet to a constant value of its gauge-invariant superfield strength, we demonstrate the generation of a chiral superpotential, upon elimination of the auxiliary superfields and dualisation of the complex linear multiplets into chiral ones. Our analysis uncovers a N = 2 superspace origin for the results recently obtained in hep-th/0601165.