# Behaviors of two supersymmetry breaking scales in $\mathcal{N}=2$ supergravity

## TL;DR

This paper investigates the patterns of supersymmetry breaking in four-dimensional  gauged supergravity with multiple vector multiplets and a hypermultiplet, deriving gravitino masses and analyzing conditions for partial and full breaking.

## Contribution

It provides explicit formulas for gravitino masses in general gaugings and explores various supersymmetry breaking patterns in models with multiple vector multiplets.

## Key findings

- Partial breaking occurs when the third derivative of the prepotential exists at the vacuum.
- Full () breaking can occur even if the third derivative of the prepotential is nontrivial.
- The results generalize previous findings to models with multiple vector multiplets.

## Abstract

We study the supersymmetry breaking patterns in four-dimensional $\mathcal{N}=2$ gauged supergravity. The model contains multiple (Abelian) vector multiplets and a single hypermultiplet which parametrizes SO$(4,1)/{\rm{SO}}(4)$ coset. We derive the expressions of two gravitino masses under {\it{general}} gaugings and prepotential based on the embedding tensor formalism, and discuss their behaviors in some concrete models. Then we confirm that in a single vector multiplet case, the partial breaking always occurs when the third derivative of the prepotential exists at the vacuum, which is consistent with the result of Ref.~\cite{Antoniadis:2018blk}, but we can have several breaking patterns otherwise. The discussion is also generalized to the case of multiple vector multiplets, and we found that the full ($\mathcal{N}=0$) breaking occurs even if the third derivative of the prepotential is nontrivial.