Long N=2, 4 multiplets in supersymmetric mechanics

TL;DR

This paper introduces a new class of long multiplets in supersymmetric mechanics with SU(2|1) symmetry, providing their superfield formulation and constructing their most general actions, expanding the understanding of supersymmetric multiplet structures.

Contribution

It defines and formulates long N=2, d=1 multiplets with non-zero external spins, including their superfield description and general actions, and explores an example of long N=4, d=1 multiplet.

Findings

Superfield formulation for long N=2, d=1 multiplets established.

Most general superfield actions for these multiplets constructed.

Example of long N=4, d=1 multiplet analyzed in detail.

Abstract

We define SU(2|1) supermultiplets described by chiral superfields having non-zero external spins with respect to SU(2) \subset SU(2|1) and show that their splitting into N=2, d=1 multiplets contains the so called "long" indecomposable N=2, d=1 multiplets (2, 4, 2)_l. We give superfield formulation for this type of N=2 long multiplets and construct their most general superfield action. A simple example of long N=4, d=1 multiplet is also considered, both in the superfield and the component formulations.