Effective Action of the N = 2 Maxwell Multiplet in Harmonic Superspace

TL;DR

This paper develops a method within harmonic superspace to compute the off-shell effective action of N=2 abelian gauge superfields, revealing distinct holomorphic and non-holomorphic quantum corrections depending on hypermultiplet mass.

Contribution

It introduces a manifestly N=2 supersymmetric harmonic supergraph technique for calculating low-energy effective actions, including quantum corrections for massless and massive hypermultiplets.

Findings

Non-holomorphic corrections for massless hypermultiplets match the supersymmetric Heisenberg-Euler Lagrangian.

Holomorphic corrections for massive hypermultiplets align with Seiberg's quantum corrections.

Method enables systematic off-shell effective action calculations in N=2 supersymmetric theories.

Abstract

We present, in the N=2, D=4 harmonic superspace formalism, a general method for constructing the off-shell effective action of an N=2 abelian gauge superfield coupled to matter hypermultiplets. Using manifestly N=2 supersymmetric harmonic supergraph techniques, we calculate the low-energy corrections to the renormalized one-loop effective action in terms of N=2 (anti)chiral superfield strengths. For a harmonic gauge prepotential with vanishing vacuum expectation value, corresponding to massless hypermultiplets, the only non-trivial radiative corrections to appear are non-holomorphic. For a prepotential with non-zero vacuum value, which breaks the U(1)-factor in the N=2 supersymmetry automorphism group and corresponds to massive hypermultiplets, only non-trivial holomorphic corrections arise at leading order. These holomorphic contribution are consistent with Seiberg's quantum correction to the effective action, while the first non-holomorphic contribution in the massless case is the N=2 supersymmetrization of the Heisenberg-Euler effective Lagrangian.