Broken symmetries from minimally doubled fermions

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. The restoration of these symmetries and the approach to the continuum limit thus require the fine-tuning of several parameters. With some assumptions, we show that this behavior is expected for actions displaying minimal fermion doubling.