Spontaneous N=2 --> N=1 local supersymmetry breaking with surviving local gauge group

TL;DR

The work shows that $N=2$ local supersymmetry can spontaneously break to $N=1$ with zero vacuum energy and a surviving compact gauge group by gauging a two-parameter $\mathbb{R}^2$ isometry of the quaternionic hypermultiplet manifold in a carefully chosen symplectic basis. Using the Calabi–Vesentini embedding of $SL(2,\mathbb{R})\otimes SO(2,n)$ into $Sp(2n+4,\mathbb{R})$, the authors realize the partial breaking through a classical super-Higgs mechanism where the graviphoton and a second vector become massive, while a compact subgroup commuting with the translations (e.g., $SO(m-1)$) remains unbroken. They provide explicit calculations on the quaternionic manifold $SO(4,m)/[SO(4)\otimes SO(m)]$, including Killing vectors and momentum maps in Alekseevskii’s formalism, showing that a Minkowski vacuum with $N=1$ is achievable and stable. The results generalize previous examples to theories with $n+1$ vector multiplets and $m$ hypermultiplets and highlight the central role of symplectic basis choice in enabling partial breaking, with potential connections to string dualities and nonperturbative $N=2$ dynamics.

Abstract

Generic partial supersymmetry breaking of $N=2$ supergravity with zero vacuum energy and with surviving unbroken arbitrary gauge groups is exhibited. Specific examples are given.

Figures (1)

• Figure 1: Scalar Potential Vs y generic and b coefficient of $e_0$