Supergravity and Supersymmetry Breaking in Four and Five Dimensions

TL;DR

This paper explores supersymmetry breaking mechanisms in heterotic string compactifications, comparing four- and five-dimensional perspectives, and derives implications for supergravity and soft breaking terms.

Contribution

It provides a detailed analysis of supersymmetry breaking in heterotic string models from both 4D and 5D viewpoints, including derivation of soft terms and higher-order effects.

Findings

Consistent 4D supergravity from 5D gauge sectors

Higher-order terms modify gauge kinetic functions

Supersymmetry breaking linked to condensates on walls

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 $\kappa^{2/3}$ 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.