Supergravity and Supersymmetry Breaking in Four and Five Dimensions

Abstract We discuss supersymmetry breaking in the field-theoretical limit of the strongly coupled heterotic string compactified on a Calabi–Yau manifold, from the different perspectives of four and five dimensions. The former applies to light degrees of freedom below the threshold for five-dimensional Kaluza–Klein excitations, whereas the five-dimensional perspective is also valid up to the Calabi–Yau scale. We show how, in the latter case, two gauge sectors separated in the fifth dimension are combined to form a consistent four-dimensional supergravity. In the lowest order of the κ 2/3 expansion, we show how a four-dimensional supergravity with gauge kinetic function f 1,2 = S is reproduced, and we show how higher-order terms give rise to four-dimensional operators that differ in the two gauge sectors. In the four-dimensional approach, supersymmetry is seen to be broken when condensates form on one or both walls, and the goldstino may have a non-zero dilatino component. As in the five-dimensional approach, the Lagrangian is not a perfect square, and we have not identified a vacuum with broken supersymmetry and zero vacuum energy. We derive soft supersymmetry-breaking terms for non-standard perturbative embeddings, that are relevant in more general situations such as type I/type IIB orientifold models.