Deformed Supersymmetric Mechanics

TL;DR

This paper constructs new N=4, d=1 supersymmetric models using superfields on SU(2|1) cosets, exploring their classical and quantum properties and linking them to non-standard supersymmetries, with potential generalizations to N=8.

Contribution

It introduces a novel superfield approach to deformed supersymmetric mechanics based on SU(2|1), connecting weak supersymmetry with standard models and extending to SU(2|2) for N=8.

Findings

Classical and quantum analysis of (1,4,3) and (2,4,2) models

Reproduction of weak supersymmetry within the superfield framework

Potential extension to N=8 supersymmetry with SU(2|2)

Abstract

Motivated by a recent interest in curved rigid supersymmetries, we construct a new type of N=4, d=1 supersymmetric systems by employing superfields defined on the cosets of the supergroup SU(2|1). The relevant worldline supersymmetry is a deformation of the standard N=4, d=1 supersymmetry by a mass parameter m. As instructive examples we consider, at the classical and quantum levels, the models associated with the supermultiplets (1,4,3) and (2,4,2) and find out interesting interrelations with some previous works on non-standard d=1 supersymmetry. In particular, the d=1 systems with "weak supersymmetry" are naturally reproduced within our SU(2|1) superfield approach as a subclass of the (1,4,3) models. A generalization to the N=8, d=1 case implies the supergroup SU(2|2) as the candidate deformed worldline supersymmetry.