Broken Symmetries from Minimally Doubled Fermions

TL;DR

This paper investigates minimally doubled fermion actions with chiral symmetry, revealing that they break discrete symmetries like parity and time-reversal, leading to the need for fine-tuning to restore symmetries in the continuum limit.

Contribution

The study analyzes the symmetry properties and renormalization behavior of novel minimally doubled fermion actions, showing the unavoidable symmetry breaking and fine-tuning requirements.

Findings

Discrete symmetries are explicitly broken in these actions.

Relevant and marginal operators are generated radiatively.

Symmetry restoration requires fine-tuning of parameters.

Abstract

Novel chirally symmetric fermion actions containing the minimum amount of fermion doubling have been recently proposed in the literature. We study the symmetries and renormalization of these actions and find that in each case, discrete symmetries, such as parity and time-reversal, are explicitly broken. Consequently, when the gauge interactions are included, these theories radiatively generate relevant and marginal operators. Thus the restoration of these symmetries and the approach to the continuum limit require the fine-tuning of several parameters. With some assumptions, we show that this behavior is unavoidable for actions displaying minimal fermion doubling.