Chiral Fermions on Quantum Four-Spheres

TL;DR

This paper develops a framework for chiral fermions on quantum four-spheres using q-deformed calculus, providing explicit constructions of wave functions, the Dirac operator, and chiral properties.

Contribution

It introduces a covariant q-deformed differential calculus for quantum four-spheres and constructs chiral fermions with a massless Dirac operator anti-commuting with gamma_5.

Findings

Eigenvalues of the Dirac operator are explicitly evaluated.

Chiral fermions are successfully defined with proper chiral symmetry.

The framework maintains SO(5)_q covariant structure.

Abstract

We construct wave functions and Dirac operator of spin $1/2$ fermions on quantum four-spheres. The construction can be achieved by the q-deformed differential calculus which is manifestly $SO(5)_q$ covariant. We evaluate the engenvalue of the Dirac operator on wave functions of the spinors and show that we can define the chiral fermions in such a way that the massless Dirac operator anti-commutes with $\gamma_5$.