Integrable Models and Supersymmetry Breaking

TL;DR

This paper explores integrable models derived from scalar-gravity theories with broken supersymmetry, analyzing their solutions to understand string coupling behavior and potential corrections in non-supersymmetric string compactifications.

Contribution

It introduces integrable dynamical systems from scalar-gravity Lagrangians with broken supersymmetry potentials, providing insights into their solution space and potential for controlling string coupling and curvature.

Findings

String coupling remains bounded in certain integrable solutions.

Unbounded string coupling and curvature occur in some static compactifications.

Higher-derivative corrections may tame large scalar curvatures.

Abstract

We elaborate on integrable dynamical systems from scalar-gravity Lagrangians that include the leading dilaton tadpole potentials of broken supersymmetry. In the static Dudas-Mourad compactifications from ten to nine dimensions, which rest on these leading potentials, the string coupling and the space-time curvature become unbounded in some regions of the internal space. On the other hand, the string coupling remains bounded in several corresponding solutions of these integrable models. One can thus identify corrected potential shapes that could grant these features generically when supersymmetry is absent or non-linearly realized. On the other hand, large scalar curvatures remain present in all our examples. However, as in other contexts, the combined effects of the higher-derivative corrections of String Theory could tame them.