Non-linearly realized discrete symmetries

TL;DR

This paper investigates how non-linearly realized discrete symmetries produce highly suppressed potentials for associated Goldstone bosons, contrasting with continuous symmetries which lack potentials.

Contribution

It analyzes different discrete symmetries to determine the extent of potential suppression in their non-linear realizations.

Findings

Potential generated from quantum corrections is highly suppressed for discrete symmetries.

Non-linear realizations of discrete symmetries feature non-derivative interactions.

The suppression level varies depending on the specific discrete symmetry studied.

Abstract

While non-linear realizations of continuous symmetries feature derivative interactions and have no potential, non-linear realizations of discrete symmetries feature non-derivative interactions and have a highly suppressed potential. These Goldstone bosons of discrete symmetries have a non-zero potential, but the potential generated from quantum corrections is inherently very highly suppressed. We explore various discrete symmetries and to what extent the potential is suppressed for each of them.