Reducing the number of counterterms with new minimally doubled actions

TL;DR

This paper explores a class of minimally doubled lattice actions with adjustable parameters, demonstrating that certain parameter choices can eliminate counterterms, potentially simplifying simulations and reducing computational costs.

Contribution

It introduces parameter-dependent minimally doubled actions that can reduce or eliminate counterterms, offering a new approach to more efficient lattice fermion formulations.

Findings

Counterterm coefficients vanish along specific parameter curves

Actions with fewer counterterms are constructible within the parameter space

Next-to-nearest-neighbor actions depend on four parameters for further optimization

Abstract

We study a class of nearest-neighbor minimally doubled actions which depend on 2 continuous parameters. We calculate the contributions of the 3 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 2 counterterms instead of the 3 of the standard Karsten-Wilczek or Borici-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 4 continuous parameters, as a further possibility in the search for renormalized actions with no counterterms.