Symanzik effective action for Karsten-Wilczek minimally doubled fermions

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.