Modified N=2 supersymmetry and Fayet-Iliopoulos terms

TL;DR

This paper explores the realization of N=2 supersymmetry in abelian gauge theories with electric and magnetic Fayet-Iliopoulos terms, revealing partial spontaneous breaking and duality transformations within manifestly supersymmetric frameworks.

Contribution

It introduces a duality-transformed superfield form of the N=2 Maxwell action with FI terms and analyzes off-shell and on-shell supersymmetry breaking mechanisms.

Findings

Off-shell N=2 supersymmetry is realized in a partial breaking mode.

Duality transformation relates electric and magnetic FI terms.

Off-shell algebra is modified on gauge-variant objects.

Abstract

We study peculiarities of realization of N=2 supersymmetry in N=2 abelian gauge theory with two sorts of FI terms, electric and magnetic ones, within manifestly supersymmetric formulations via the Mezincescu and harmonic-analytic prepotentials. We obtain a `magnetic', duality- transformed superfield form of the N=2 Maxwell effective holomorphic action with standard electric $FI$ term and demonstrate that in such a system off-shell N=2 supersymmetry is inevitably realized in an unusual Goldstone mode corresponding to the {\it partial} spontaneous breaking down to N=1. On shell, the standard total breaking occurs. In a system with the two sorts of FI terms, off-shell N=2 supersymmetry is realized in the partial breaking mode both in the electric and magnetic representations. This regime is retained on shell due to the Antoniadis- Partouche-Taylor mechanism. We show that the off-shell algebra of N=2 supersymmetry in the partial breaking realization is modified on gauge-variant objects like potentials and prepotentials. The closure of spinor charges involves some special gauge transformations before any gauge-fixing.