Geometry and beta-functions for N=2 matter models in two dimensions

TL;DR

This paper investigates the geometry and renormalization properties of N=2 supersymmetric nonlinear sigma-models in two dimensions, identifying conditions for conformal invariance and enhanced N=4 supersymmetry.

Contribution

It provides a detailed analysis of the geometric structure and one-loop beta-functions of N=2 models, revealing criteria for models to be conformally invariant with N=4 supersymmetry.

Findings

Identified geometric conditions for vanishing beta-functions.

Derived one-loop divergences in superspace formalism.

Established link between N=2 and N=4 supersymmetry in these models.

Abstract

We study renormalizable nonlinear sigma-models in two dimensions with N=2 supersymmetry described in superspace in terms of chiral and complex linear superfields. The geometrical structure of the underlying manifold is investigated and the one-loop divergent contribution to the effective action is computed. The condition of vanishing beta-function allows to identify a class of models which satisfy this requirement and possess N=4 supersymmetry.