Algorithmic Boundedness-From-Below Conditions for Generic Scalar Potentials

Understand

Checking that a scalar potential is bounded from below (BFB) is an ubiquitous and notoriously difficult task in many models with extended scalar sectors.

• Exact analytic BFB conditions are known only in simple cases.
• In this work, we present a novel approach to algorithmically establish the BFB conditions for any polynomial scalar potential.
• The method relies on elements of multivariate algebra, in particular, on resultants and on the spectral theory of tensors, which is being developed by the mathematical community.