Dirac operator on the quantum fuzzy four-sphere $ S_{qF}^{4} $

TL;DR

This paper develops and analyzes q-deformed Dirac and chirality operators on the quantum fuzzy four-sphere, ensuring their consistency with classical limits and exploring their properties in instanton sectors.

Contribution

It introduces q-deformed fuzzy Dirac and chirality operators on the quantum fuzzy four-sphere using the Ginsparg-Wilson algebra, including gauged versions and instanton sector analysis.

Findings

Operators have correct commutative limit as q→1 and l→∞.

Constructed gauged Dirac and chirality operators in instanton sectors.

Validated the consistency of q-deformed operators with classical geometry.

Abstract

The q-deformed fuzzy Dirac and chirality operators on quantum fuzzy four-sphere $ S^{4}_{qF} $. Using the q-deformed fuzzy Ginsparg-Wilson algebra, it has been studied the q-deformed fuzzy Dirac and chirality operators in instanton and no-instanton sector. Also, gauged Dirac and chirality operators in both cases have been constructed. It has been showed that In each step our results have correct commutative limit in the limit case when $ q\longrightarrow1 $ and noncommutative parameter $ l $ tends to infinity.