Non-Perturbative Aspects of Spontaneous Symmetry Breaking

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 ${\phi }^4$ 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 ${\phi }^4$ 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.

corrections and new section added

References in corpus (9)

• Ultra-Light Dark Matter
• Higgs-field Portal into Hidden Sectors
• A second Higgs from the Higgs portal
• Dark matters on the scale of galaxies
• Safety in darkness: Higgs portal to simple Yukawa systems
• Impact of Higgs portal on gravity-mediated production of superheavy dark matter
• Constraining Nonthermal Dark Matter's Impact on the Matter Power Spectrum
• Power meets Precision to explore the Symmetric Higgs Portal
• Search for hidden-photon Dark Matter with FUNK