Gauging N=4 Supersymmetric Mechanics

TL;DR

This paper explores off-shell dualities in N=4 supersymmetric mechanics, demonstrating how gauging symmetries with superfields leads to new multiplets and hyper-Kähler metrics, enriching the understanding of supersymmetric models.

Contribution

It introduces a supersymmetric gauging procedure for N=4 mechanics, revealing new multiplets and metrics, including a nonlinear (4,4,0) variant producing hyper-Kähler geometries.

Findings

Gauging symmetries relates different supermultiplets.

Generated hyper-Kähler metrics with isometries.

Established new nonlinear multiplet variants.

Abstract

We argue that off-shell dualities between d=1 supermultiplets with different sets of physical bosonic components and the same number of fermionic ones are related to gauging some symmetries in the actions of the supermultiplets with maximal sets of physical bosons. Our gauging procedure uses off-shell superfields and so is manifestly supersymmetric. We focus on N=4 supersymmetric mechanics and show that various actions of the multiplet (3,4,1) amount to some gauge choices in the gauged superfield actions of the linear or nonlinear (4,4,0) multiplets. In particular, the conformally invariant (3,4,1) superpotential is generated by the Fayet-Iliopoulos term of the gauge superfield. We find a new nonlinear variant of the multiplet (4,4,0), such that its simplest superfield action produces the most general 4-dim hyper-K\"ahler metric with one triholomorphic isometry as the bosonic target metric. We also elaborate on some other instructive examples of N=4 superfield gaugings, including a non-abelian gauging which relates the free linear (4,4,0) multiplet to a self-interacting (1,4,3) multiplet.