On the quantization of the N=2 supersymmetric non linear sigma model

TL;DR

This paper develops a covariant and N=2 supersymmetric quantization method for the 2D non-linear sigma model, deriving conditions on the metric and dilaton from superconformal symmetry.

Contribution

It introduces a new quantization approach that preserves covariance and supersymmetry, and derives geometric constraints from superconformal algebra.

Findings

Dilaton is shown to be constant under superconformal symmetry

The method maintains covariance and supersymmetry during quantization

Explicit OPE calculations include the dilaton contribution

Abstract

A method for quantizing the bidimensional N=2 supersymmetric non-linear sigma model is developed. This method is both covariant under coordinate transformations (concerning the order relevant for calculations) and explicitly N=2 supersymmetric. The OPE of the supercurrent is computed accordingly, including also the dilaton. By imposing the N=2 superconformal algebra the equations for the metric and dilaton are obtained. In particular, they imply that the dilaton is a constant.