Symanzik effective action for Karsten-Wilczek minimally doubled fermions

TL;DR

The paper builds the Symanzik effective action for Karsten–Wilczek minimally doubled fermions, making the two tastes explicit via Creutz point-splitting and analyzing the lattice symmetries to restrict allowed operators up to dimension-5. It treats both free and interacting KW fermions, showing that dimension-3 (divergent) operators survive in the continuum limit and must be absorbed by renormalization, while dimension-4 and dimension-5 operators include derivative, mass, and gluonic terms. In the interacting case, two purely gluonic dimension-4 operators appear, and the operator basis for higher dimensions uses covariant derivatives $D_ u$. This framework provides the necessary foundation for lattice χPT with KW fermions and highlights challenges in taste interpretation, suggesting future exploration of alternative point-splittings and spurion-based analyses to determine low-energy constants from lattice data.

Abstract

Karsten-Wilczek (KW) fermions are a popular variant of minimally doubled fermions. We construct Symanzik effective action for KW fermions, which is known to break the hypercubic symmetry of the lattice action. In this work we make the two fermionic modes, called tastes, explicit using the point-splitting proposal of Creutz and Misumi and write the KW action in terms of the taste fields. We identify the symmetries of the point-split action and write down the Symanzik effective action up to dimension-5, including the divergent dimension-3, operators for both free and interacting KW fermions.