Proving the Absence of the Perturbative Corrections to the N=2 U(1) K\"ahler Potential Using the N=1 Supergraph Techniques

TL;DR

This paper proves that in N=2 supersymmetric U(1) gauge theory, the Kahler potential receives no perturbative corrections, using N=1 supergraph techniques to confirm the non-renormalization theorem.

Contribution

It demonstrates the absence of perturbative corrections to the Kahler potential in N=2 U(1) gauge theory through supergraph methods, providing a new proof of the non-renormalization theorem.

Findings

No perturbative corrections to the Kahler potential are found.

Supergraph techniques effectively prove non-renormalization in N=2 theories.

The proof applies to theories with general prepotential F().

Abstract

Perturbative N=2 non-renormalization theorem states that there is no perturbative correction to the Kahler potential \int d^4\theta K(\Phi,\bar{\Phi}). We prove this statement by using the N=1 supergraph techniques. We consider the N=2 supersymmetric U(1) gauge theory which possesses general prepotential F(\Psi).