Vacuum Stability Conditions and Potential Minima for a Matrix Representation in Lightcone Orbit Space

Abstract

The orbit space for a scalar field in a complex square matrix representation obtains a Minkowski space structure from the Cauchy-Schwarz inequality. It can be used to find vacuum stability conditions and minima of the scalar potential. The method is suitable for fields such as a bidoublet, an $SU(2)$ triplet or $SU(3)$ octet. We use the formalism to find the vacuum stability conditions for the left-right symmetric potential of a bidoublet and left and right Higgs doublets.

17 pages, 3 figures, typos corrected

References in corpus (3)

• Properties of the general NHDM. I. The orbit space
• Baryogenesis in the two doublet and inert singlet extension of the Standard Model
• Left-Right Symmetric Model without Higgs Triplets