Copositivity for 3rd order symmetric tensors and applications

Abstract

The strict opositivity of 4th order symmetric tensor may apply to detect vacuum stability of general scalar potential. For finding analytical expressions of (strict) opositivity of 4th order symmetric tensor, we may reduce its order to 3rd order to better deal with it. So, it is provided that several analytically sufficient conditions for the copositivity of 3th order 2 dimensional (3 dimensional) symmetric tensors. Subsequently, applying these conclusions to 4th order tensors, the analytically sufficient conditions of copositivity are proved for 4th order 2 dimensional and 3 dimensional symmetric tensors. Finally, we apply these results to present analytical vacuum stability conditions for vacuum stability for ${\mathbb{Z}}_3$ scalar dark matter.

21 pages

References in corpus (4)

• Minimal semi-annihilating ${\mathbb{Z}}_N$ scalar dark matter
• Boundedness from below in the $U(1)\times U(1)$ three-Higgs-Doublet model
• Polynomial complementarity problems
• Analytical expressions of copositivity for 4th order symmetric tensors and applications

Cited by in corpus (4)

• Vacuum stability conditions of the general two-Higgs-doublet potential
• Positivity Conditions for Cubic, Quartic and Quintic Polynomials
• Copositivity for a class of fourth order symmetric tensors given by scalar dark matter
• Co-positivity of tensors and bounded from below conditions of CP conserving two-Higgs-doublet potential