Operator ordering in Two-dimensional N=1 supersymmetry with curved manifold

TL;DR

This paper addresses the operator ordering problem in two-dimensional N=1 supersymmetric models with curved target spaces, demonstrating that the super-Poincaré algebra determines the correct ordering and algebra extensions.

Contribution

It shows how the super-Poincaré algebra fixes the operator ordering in curved supersymmetric models, ensuring correct supersymmetry algebra realization.

Findings

Supercurrent with proper operator ordering derived

Central extension of supersymmetry algebra obtained

Operator ordering problem resolved in curved target spaces

Abstract

We investigate an operator ordering problem in two-dimensional N=1 supersymmetric model which consists of n real superfields. There arises an operator ordering problem when the target space is curved. We have to fix the ordering in quantum operator properly to obtain the correct supersymmetry algebra. We demonstrate that the super-Poincar\'{e} algebra fixes the correct operator ordering. We obtain a supercurrent with correct operator ordering and a central extension of supersymmetry algebra.