We study a class of nearest-neighbor minimally doubled actions that depend on two continuous parameters. We calculate the contributions of the three possible counterterms in perturbation theory, and we find that for each counterterm there are curves in the parameter space on which its coefficient vanishes. One can thus construct renormalized actions that contain only two counterterms, instead of the three of the standard Karsten-Wilczek or Boriçi-Creutz actions. Our investigations suggest the usefulness of analogous nonperturbative searches for values of the parameters for which the number of counterterms can be reduced. They can also be an inspiration to undertake a search for ultralocal minimally doubled actions with even better counterterm-reducing properties, including the optimal case in which all counterterms can be removed. Simulations of the latter actions will be much cheaper than the cases in which one needs to add counterterms to the bare actions, like the already conveniently inexpensive standard Karsten-Wilczek fermions. Finally, we also introduce minimally doubled fermions with next-to-nearest-neighbor interactions, which depend on four continuous parameters, as a further possibility in the search for renormalized actions with no counterterms.

• Received 6 September 2013

DOI:https://doi.org/10.1103/PhysRevD.89.014501