Couplings of ${\cal N}=4$, $d=1$ mirror supermultiplets

TL;DR

This paper constructs and analyzes models of coupled mirror supermultiplets in ${ m N}=4$, $d=1$ supersymmetric mechanics, revealing new interactions and equations such as the Nahm equations, with potential for deformation to SU(2|1) supersymmetry.

Contribution

It introduces new coupled models of mirror supermultiplets in ${ m N}=4$, $d=1$ supersymmetry, including the derivation of Nahm equations and generalization to SU(2|1) deformation.

Findings

Coupled mirror multiplets lead to Nahm equations for spin variables.

Models admit generalization to SU(2|1) supersymmetry.

Construction of new supersymmetric mechanics models with mirror multiplets.

Abstract

We construct models of coupled semi-dynamical (spin) and dynamical mirror multiplets of ${\cal N}=4$ supersymmetric mechanics in $d=1$ harmonic superspace. Specifically, we consider a semi-dynamical mirror multiplet ${\bf (3,4,1)}$ coupled to dynamical mirror multiplets ${\bf (1, 4, 3)}$ and ${\bf (2, 4, 2)}$. Coupling of the multiplets ${\bf (3, 4, 1)}$ and ${\bf (1, 4, 3)}$ yields a mirror counterpart of the earlier constructed model implying the Nahm equations for the spin variables with the bosonic component of the multiplet ${\bf (1, 4, 3)}$ as an evolution parameter. We also couple the mirror multiplet ${\bf (2,4,2)}$ to the mirror semi-dynamical multiplet ${\bf (3, 4, 1)}$ using chiral ${\cal N}=4$ superspace. The models constructed admit a generalization to the SU$(2|1)$ deformation of ${\cal N}=4$, $d=1$ Poincar\'e supersymmetry.