Observations on the Partial Breaking of $N=2$ Rigid Supersymmetry

TL;DR

This paper investigates the conditions under which partial breaking of N=2 rigid supersymmetry occurs in theories with abelian vector multiplets, emphasizing the role of symplectic structure and Fayet-Iliopoulos terms.

Contribution

It provides invariant conditions for partial supersymmetry breaking based on a quartic Fayet-Iliopoulos charge invariant and modifies the N=2 symmetry algebra with a vector central charge.

Findings

Identifies symplectic invariant conditions for supersymmetry breaking.

Highlights the importance of Fayet-Iliopoulos terms and the quartic invariant.

Shows the algebra is modified by a vector central charge.

Abstract

We study the partial breaking of $N=2$ rigid supersymmetry for a generic rigid special geometry of $n$ abelian vector multiplets in the presence of Fayet-Iliopoulos terms induced by the Hyper-K\"ahler momentum map. By exhibiting the symplectic structure of the problem we give invariant conditions for the breaking to occur, which rely on a quartic invariant of the Fayet-Iliopoulos charges as well as on a modification of the $N=2$ rigid symmetry algebra by a vector central charge.