Electrically gauged $ \mathcal{N}=4 $ supergravities in D = 4 with $ \mathcal{N}=2 $ vacua

Abstract

We study $ \mathcal{N}=2 $ vacua in spontaneously broken $ \mathcal{N}=4 $ electrically gauged supergravities in four space-time dimensions. We argue that the classification of all such solutions amounts to solving a system of purely algebraic equations. We then explicitly construct a special class of consistent $ \mathcal{N}=2 $ solutions and study their properties. In particular we find that the spectrum assembles in $ \mathcal{N}=2 $ massless or BPS supermultiplets. We show that (modulo U(1) factors) arbitrary unbroken gauge groups can be realized provided that the number of $ \mathcal{N}=4 $ vector multiplets is large enough. Below the scale of partial supersymmetry breaking we calculate the relevant terms of the low-energy effective action and argue that the special Kähler manifold for vector multiplets is completely determined, up to its dimension, and lies in the unique series of special Kähler product manifolds.