Self-interacting scalar fields at high-temperature

TL;DR

This paper investigates high-temperature behaviors of self-interacting scalar fields using lattice path integrals, with applications to modeling strong interactions, confinement, and dark matter phenomena.

Contribution

It introduces a lattice path integral approach to scalar fields at high temperature, modeling strong interactions, confinement, and dark matter effects.

Findings

Reproduces known potentials validating the method

Models confinement scale emergence from conformal Lagrangian

Explains flat galaxy rotation curves without non-baryonic matter

Abstract

We study two self-interacting scalar field theories in their high-temperature limit using path integrals on a lattice. We first discuss the formalism and recover known potentials to validate the method. We then discuss how these theories can model, in the high-temperature limit, the strong interaction and General Relativity. For the strong interaction, the model recovers the known phenomenology of the nearly static regime of heavy quarkonia. The model also exposes a possible origin for the emergence of the confinement scale from the approximately conformal Lagrangian. Aside from such possible insights, the main purpose of addressing the strong interaction here --given that more sophisticated approaches already exist-- is mostly to further verify the pertinence of the model in the more complex case of General Relativity for which non-perturbative methods are not as developed. The results have important implications on the nature of Dark Matter. In particular, non-perturbative effects naturally provide flat rotation curves for disk galaxies, without need for non-baryonic matter, and explain as well other observations involving Dark Matter such as cluster dynamics or the dark mass of elliptical galaxies.