Symanzik effective action for Karsten-Wilczek minimally doubled fermions

TL;DR

This paper develops a Symanzik effective action for Karsten-Wilczek fermions, explicitly incorporating taste degrees of freedom and analyzing symmetry breaking effects up to dimension-5 operators.

Contribution

It constructs the Symanzik effective action for KW fermions with explicit taste fields, including symmetry analysis and operators up to dimension-5.

Findings

Explicit taste formulation of KW fermions

Identification of symmetry properties of the point-split action

Derivation of the effective action including divergent operators

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.