The $$ \mathcal{N} = 1 $$ low-energy effective action of spontaneously broken $$ \mathcal{N} = 2 $$ supergravities

Abstract

We consider the class of four-dimensional N=2 gauged supergravities whose maximally symmetric ground states leave only one of the two supersymmetries intact. For these theories we derive the low-energy effective action below the scale of partial supersymmetry breaking and compute the N=1 couplings in terms of the N=2 'input data'. We show that this effective action satisfies the constraints of N=1 supergravity in that its sigma-model metric is Kahler, while the superpotential and the gauge kinetic functions are holomorphic. As an example we discuss the N=1 effective supergravity of type II compactifications.