Fuzzy AdS-conifold $Y_{Ad{S}_F}^6$ and Dirac operator of principal fibration $X_{Ad{S}_F}^5\to Ad{S}_F^2\times Ad{S}_F^2$

Abstract

It has been constructed fuzzy AdS- conifold $Y_{Ad{S}_F}^6$ on the base $Ad{S}_F^3\times Ad{S}_F^2$ which is topologically homeomorphic with the total space of the fibration $X_{Ad{S}_F}^5\to Ad{S}_F^2\times Ad{S}_F^2$. After the projective module description of this bundle, the pseudo fuzzy Dirac and chirality operators on fuzzy $Ad{S}_F^2\times Ad{S}_F^2$ 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.

arXiv admin note: text overlap with arXiv:2003.05737