N=2 sigma model Action on Non(anti)commutative Superspace

TL;DR

This paper demonstrates how to resum the infinite series in the classical action of non(anti)commutative N=2 sigma models in two dimensions, revealing a standard form and a smeared target space due to deformation.

Contribution

It introduces a method to resum the infinite series in the action using auxiliary field constraints, clarifying the structure of non(anti)commutative sigma models.

Findings

The action can be expressed in a standard form after resummation.

The target space geometry is modified ('smeared') by the deformation parameter.

Resummation simplifies the analysis of non(anti)commutative supersymmetric models.

Abstract

We show that the infinite series in the classical action for non(anti)commutative N=2 sigma models in two dimensions, can be resummed by using constraint equations of the auxiliary fields. We argue that the resulting action takes a standard form and the target space is necessarily smeared by terms dependent on the deformation parameter.