Discrete Symmetries Excluded by Quantum Breaking

TL;DR

This paper demonstrates that theories with spontaneously broken discrete symmetries face a fundamental inconsistency due to the combined constraints of cosmological domain walls and quantum de Sitter breaking, limiting many Standard Model extensions.

Contribution

It shows that discrete symmetries either lead to domain wall problems or inconsistent de Sitter minima, ruling out many models with such symmetries.

Findings

Discrete symmetries are incompatible with quantum de Sitter breaking.

Many Standard Model extensions with discrete symmetries are excluded.

Either exact or approximate discrete symmetries lead to fundamental issues.

Abstract

In this note we show that the cosmological domain wall and the de Sitter quantum breaking problems complement each other in theories with discrete symmetries that are spontaneously broken at low energies. Either the symmetry is exact and there is a domain wall problem, or it is approximate and there exists an inconsistent de Sitter minimum. This leaves no room for many extension of the Standard Model based on such discrete symmetries. We give some examples that include NMSSM, spontaneous CP violation at the weak scale and some versions of the Peccei-Quinn scenario with discrete symmetries.