Construction of supercharges for the one-dimensional supersymmetric nonlinear sigma model

TL;DR

This paper clarifies the construction of supercharges in one-dimensional supersymmetric nonlinear sigma models, resolving ambiguities in defining hidden supersymmetries and ensuring their correct algebraic realization.

Contribution

It introduces a consistent method to define supercharges and supersymmetries simultaneously, addressing ambiguities caused by partial integrations in superspace.

Findings

Resolved ambiguities in supercharge definitions

Established a consistent framework for hidden supersymmetries

Provided new results on supercharge construction

Abstract

This paper addresses an issue essential to the study of hidden supersymmetries (meaning here ones that do not close on the Hamiltonian) for one-dimensional non-linear supersymmetric sigma models. The issue relates to ambiguities, due to partial integrations in superspace, both in the actual definition of these supersymmetries and in the Noether definition of the associated supercharges. The unique consistent forms of both these definitions have to be determined simultaneously by a process that adjusts the former definitions so that the associated supercharges do indeed correctly generate them with the aid of the canonical formalism. The paper explains and illustrates these matters and gives some new results.