On the next-to-leading-order correction to the effective action in N=2 gauge theories

TL;DR

This paper analyzes the one-loop non-holomorphic correction to the low-energy effective action in N=2 gauge theories using harmonic superspace, confirming previous results and calculating a new coefficient, with implications for superconformal theories.

Contribution

It provides a manifestly N=2 supersymmetric calculation of the one-loop non-holomorphic correction and determines an unknown coefficient, enhancing understanding of the effective action in these theories.

Findings

One-loop correction matches previous superfield calculations.

Calculated the previously unknown coefficient of the non-holomorphic term.

Found that the correction does not vanish in superconformal theories.

Abstract

I attempt to analyse the next-to-leading-order non-holomorphic contribution to the Wilsonian low-energy effective action in the four-dimensional N=2 gauge theories with matter, from the manifestly N=2 supersymmeric point of view, by using the harmonic superspace. The perturbative one-loop correction is found to be in agreement with the N=1 superfield calculations of de Wit, Grisaru and Rocek. The previously unknown coefficient in front of this non-holomorphic correction is calculated. A special attention is devoted to the N=2 superconformal gauge theories, whose one-loop non-holomorphic contribution is likely to be exact, even non-perturbatively. This leading (one-loop) non-holomorphic contribution to the LEEA of the N=2 superconformally invariant gauge field theories is calculated, and it does not vanish, similarly to the case of the N=4 super-Yang-Mills theory.