Renormalization of minimally doubled fermions

TL;DR

This paper studies the one-loop renormalization of minimally doubled fermions, specifically Borici-Creutz and Karsten-Wilczek formulations, identifying necessary counterterms and analyzing their effects on symmetry and currents.

Contribution

It provides the first detailed one-loop renormalization analysis for these fermion formulations, including counterterm coefficients and conserved currents.

Findings

Three counterterms are needed for each formulation.

No power divergences appear in the vacuum polarization.

Counterterms cancel Lorentz symmetry breaking contributions.

Abstract

We investigate the renormalization properties of minimally doubled fermions, at one loop in perturbation theory. Our study is based on the two particular realizations of Borici-Creutz and Karsten-Wilczek. A common feature of both formulations is the breaking of hyper-cubic symmetry, which requires that the lattice actions are supplemented by suitable counterterms. We show that three counterterms are required in each case and determine their coefficients to one loop in perturbation theory. For both actions we compute the vacuum polarization of the gluon. It is shown that no power divergences appear and that all contributions which arise from the breaking of Lorentz symmetry are cancelled by the counterterms. We also derive the conserved vector and axial-vector currents for Karsten-Wilczek fermions. Like in the case of the previously studied Borici-Creutz action, one obtains simple expressions, involving only nearest-neighbour sites. We suggest methods how to fix the coefficients of the counterterms non-perturbatively and discuss the implications of our findings for practical simulations.