Gauged Dirac operator on the quantum sphere in instanton sector

Abstract

In this paper, we construct the [Formula: see text]-deformed fuzzy Dirac and chirality operators on quantum fuzzy Podles sphere [Formula: see text]. Using the [Formula: see text]-deformed fuzzy Ginsparg–Wilson algebra, we study the [Formula: see text]-deformed gauged fuzzy Dirac and chirality operators in instanton sector. We will show the correct fuzzy sphere limit in the limit case [Formula: see text] and the correct commutative limit in the limit case when [Formula: see text] and noncommutative parameter [Formula: see text] tends to infinity.