English

Geometry of Flat Directions in Scale-Invariant Potentials

High Energy Physics - Phenomenology 2019-10-03 v2

Abstract

We observe that biquadratic potentials admit non-trivial flat directions when the determinant of the quartic coupling matrix of the scalar fields vanishes. This consideration suggests a new approach to the problem of finding flat directions in scale-invariant theories, noticeably simplifying the study of scalar potentials involving many fields. The method generalizes to arbitrary quartic potentials by requiring that the hyperdeterminant of the tensor of scalar couplings be zero. We demonstrate our approach with detailed examples pertaining to common scalar extensions of the Standard Model.

Keywords

Cite

@article{arxiv.1904.07867,
  title  = {Geometry of Flat Directions in Scale-Invariant Potentials},
  author = {Kristjan Kannike and Aleksei Kubarski and Luca Marzola},
  journal= {arXiv preprint arXiv:1904.07867},
  year   = {2019}
}

Comments

6 pages, 1 figure

R2 v1 2026-06-23T08:41:48.286Z