On the D = 4, N = 2 Non-Renormalization Theorem

TL;DR

This paper provides a rigorous proof that D=4, N=2 super Yang-Mills theories do not have ultraviolet divergences beyond one loop, using harmonic superspace background field formulation, and also shows the absence of certain two-loop corrections.

Contribution

It offers the first rigorous proof of the N=2 non-renormalization theorem for general theories with matter hypermultiplets using harmonic superspace methods.

Findings

Ultraviolet divergences beyond one loop are absent in these theories.

Leading non-holomorphic corrections at two loops are absent.

The background field formulation simplifies the analysis of quantum corrections.

Abstract

Using the harmonic superspace background field formulation for general D=4, N=2 super Yang-Mills theories, with matter hypermultiplets in arbitrary representations of the gauge group, we present the first rigorous proof of the N=2 non-renormalization theorem; specifically, the absence of ultraviolet divergences beyond the one-loop level. Another simple consequence of the background field formulation is the absence of the leading non-holomorphic correction to the low-energy effective action at two loops.