Fuzzy AdS-conifold $ Y_{AdS_{F}}^{6} $ and Dirac operator of principal fibration $ X_{AdS_{F}}^{5}\rightarrow AdS_{F}^{2}\times AdS_{F}^{2} $

Abstract

It has been constructed fuzzy AdS- conifold $ Y_{AdS_{F}}^{6} $ on the base $ AdS_{F}^{3}\times AdS_{F}^{2} $ which is topologically homeomorphic with the total space of the fibration $ X_{AdS_{F}}^{5}\rightarrow AdS_{F}^{2}\times AdS_{F}^{2} $. After the projective module description of this bundle, the pseudo fuzzy Dirac and chirality operators on fuzzy $ AdS^{2}_{F}\times AdS_{F}^{2} $ have been studied. Using the fuzzy Ginsparg-Wilson algebra, it has been studied the gauged fuzzy Dirac and chirality operators in instanton sector. It has been showed that they have correct commutative limit in the limit case when noncommutative parameter $ l_{\alpha} $ tends to infinity.