Renormalization group improvement of the effective potential in six dimensions

Using the renormalization group improvement technique, we study the effective potential of a model consisting of N scalar fields ϕⁱ transforming in the fundamental representation of an O (N ) group coupled to an additional scalar field σ via cubic interactions, defined in a six-dimensional spacetime. We find that the model presents a metastable vacuum, which can be long-lived, where the particles become massive. The existence of attractive and repulsive interactions plays a crucial role in such phenomena.