The Background Field Method for N = 2 Super Yang-Mills Theories in Harmonic Superspace

TL;DR

This paper develops a background field method for N=2 super Yang-Mills theories in harmonic superspace, analyzing ghost structures and one-loop effective actions, with implications for N=4 theories and Seiberg's effective action.

Contribution

It introduces a novel background field approach in harmonic superspace for N=2 super Yang-Mills theories, detailing ghost structures and one-loop effective actions, and explores implications for N=4 theories.

Findings

Ghost structure includes fermionic and bosonic hypermultiplets in the adjoint representation.

One-loop effective action is determined solely by ghost corrections in pure super Yang-Mills.

In N=2 SU(2) theory, the low-energy one-loop effective action matches Seiberg's holomorphic effective action.

Abstract

The background field method for N=2 super Yang-Mills theories in harmonic superspace is developed. The ghost structure of the theory is investigated. It is shown that the ghosts include two fermionic real omega-hypermultiplets (Faddeev-Popov ghosts) and one bosonic real omega-hypermultiplet (Nielsen-Kallosh ghost), all in the adjoint representation of the gauge group. The one-loop effective action is analysed in detail and it is found that its structure is determined only by the ghost corrections in the pure super Yang-Mills theory. As applied to the case of N=4 super Yang-Mills theory, realized in terms of N=2 superfields, the latter result leads to the remarkable conclusion that the one-loop effective action of the theory does not contain quantum corrections depending on the N=2 gauge superfield only. We show that the leading low-energy contribution to the one-loop effective action in the N=2 SU(2) super Yang-Mills theory coincides with Seiberg's perturbative holomorphic effective action.