Aspects of Spontaneous N=2 -> N=1 Breaking in Supergravity

TL;DR

This work identifies geometric conditions on the scalar manifolds of $N=2$ supergravity that are necessary for spontaneous $N=2\to N=1$ breaking in $D=4$, focusing on Minkowski vacua. It shows that breaking requires two commuting, gauged translational ${R}^2$ isometries of the quaternionic hypermultiplet sector, along with a suitable basis where the $SU(2)$ triplet of prepotentials aligns to yield a single massless gravitino and a massive spin-$3/2$ multiplet, with the rest of the spectrum Higgsed appropriately. The authors then derive the low-energy $N=1$ theory by integrating out the heavy fields, demonstrating that the hypermultiplet quotient ${\bf M}_h/{\bf R}^2$ is Kähler and that the $N=1$ potential takes the standard holomorphic form, with Minkowski vacua enforcing $W=0$; the consistency conditions are encoded geometrically in the quotient construction and the harmonicity of gauge couplings. Overall, the paper links high-energy $N=2$ data to permissible $N=1$ effective dynamics through precise geometric constraints on the scalar manifolds.

Abstract

We discuss some issues related to spontaneous N=2-> N=1 supersymmetry breaking. In particular, we state a set of geometrical conditions which are necessary that such a breaking occurs. Furthermore, we discuss the low energy N=1 effective Lagrangian and show that it satisfies non-trivial consistency conditions which can also be viewed as conditions on the geometry of the scalar manifold.