The chiral and flavour projection of Dirac-Kahler fermions in the geometric discretization

TL;DR

This paper demonstrates how to implement exact chiral and flavour symmetries for Dirac-Kahler fermions within geometric discretization, requiring multiple complexes and new operators to achieve simultaneous projections.

Contribution

It introduces a novel approach to exact chiral and flavour projection in Dirac-Kahler fermions using geometric discretization, involving new operators and complex structures.

Findings

Exact chiral symmetry achieved with two complexes.

Flavour projection requires additional structures and operators.

Single flavour of chiral field remains after projection.

Abstract

It is shown that an exact chiral symmetry can be described for Dirac-Kahler fermions using the two complexes of the geometric discretization. This principle is extended to describe exact flavour projection and it is shown that this necessitates the introduction of a new operator and two new structures of complex. To describe simultaneous chiral and flavour projection, eight complexes are needed in all and it is shown that projection leaves a single flavour of chiral field on each.