Operator ordering and Classical soliton path in Two-dimensional N=2 supersymmetry with Kahler potential

TL;DR

This paper explores operator ordering in 2D N=2 supersymmetric models with Kahler potential, demonstrating how supersymmetry guides correct ordering, analyzing soliton paths, and examining supersymmetry breaking effects.

Contribution

It establishes the operator ordering rule via super Poincare algebra, including central extensions, and analyzes soliton paths and supersymmetry breaking in the model.

Findings

Operator ordering is fixed by supersymmetry requirements.

Soliton paths are straight lines in the superpotential's complex plane.

Half of the supersymmetry is broken by solitons.

Abstract

We investigate a 2-dimensional N=2 supersymmetric model which consists of n chiral superfields with Kahler potential. When we define quantum observables, we are always plagued by operator ordering problem. Among various ways to fix the operator order, we rely upon the supersymmetry. We demonstrate that the correct operator order is given by requiring the super Poincare algebra by carrying out the canonical Dirac bracket quantization. This is shown to be also true when the supersymmetry algebra has a central extension by the presence of topological soliton. It is also shown that the path of soliton is a straight line in the complex plane of superpotential W and triangular mass inequality holds. And a half of supersymmetry is broken by the presence of soliton.