Non-Perturbative Aspects of Spontaneous Symmetry Breaking

TL;DR

This paper explores the non-perturbative aspects of spontaneous symmetry breaking in scalar quantum field theories, revealing connections to instantons, self-dual Yang-Mills theories, and vacuum stability in the infrared limit.

Contribution

It demonstrates a natural description of instantons in scalar theories and establishes an exact map to self-dual Yang-Mills theories in the infrared limit, advancing understanding of symmetry breaking.

Findings

Scalar b4 theory describes instantons in the infrared limit.

An exact mapping between b4 and self-dual Yang-Mills theories is established.

Higher energy states become unstable, leading to vacuum transition in the Higgs portal.

Abstract

Spontaneous symmetry breaking is studied in the ultralocal limit of a scalar quantum field theory, that is when $E\approx m$ (or infrared limit). In this limit we show that a $ \varphi^4$ theory in the euclidean space in four-dimensions describes naturally instantons. Furthermore, in the infrared limit we show that there is an exact map between $ \varphi^4$ with self-dual Yang-Mills theories. The spontaneous symmetry breaking in the infrared limit for a Higgs portal is also considered and we demonstrate how states of higher energy becomes unstable and spread converting a false vacuum in a true one.