模糊AdS-conifold $ Y_{AdS_{F}}^{6} $与主纤维化的Dirac算子$ X_{AdS_{F}}^{5}\rightarrow AdS_{F}^{2}\times AdS_{F}^{2} $
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} $
摘要：
在与纤维化$ X_{AdS_{F}}^{5}\rightarrow AdS_{F}^{2}\times AdS_{F}^{2} $的全空间拓扑同胚的基$ AdS_{F}^{3}\times AdS_{F}^{2} $上构造了模糊AdS-锥$ Y_{AdS_{F}}^{6} $.在此丛的投射模描述之后，研究了模糊$ AdS^{2}_{F}\times AdS_{F}^{2} $上的伪模糊Dirac算子和手征算子.利用模糊Ginsparg-Wilson代数研究了瞬子扇区中的规范模糊Dirac算子和手征算子。证明了当非对易参数$ l_α $趋于无穷大时，它们在极限情形下有正确的对易极限。
英文摘要：
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_α $ tends to infinity.
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