Vector bundles on fuzzy K?hler manifolds
Vector bundles on fuzzy K?hler manifolds
复制标题
模糊克勒流形上的向量丛
DOI：
10.1093/ptep/ptad006
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发表时间：
2023
影响因子：
3.5
通讯作者：
Kanno Satoshi
中科院分区：
文献类型：
--
作者：
Adachi Hiroyuki;Ishiki Goro;Kanno Satoshi
给出了一般闭Kähler流形上向量丛的矩阵正则化方法。这种矩阵正则化是Berezin-Toeplitz量化的自然推广，并给出了从向量丛的部分到矩阵的映射。我们考察了该映射在大N极限下的渐近行为。对于具有代数结构的向量丛，我们得到了截断代数与大N极限上对应的矩阵代数之间的优美对应。我们给出了复射影空间CPn和环面T2n上单极子丛的两个显式例子。
We propose a matrix regularization of vector bundles over a general closed Kähler manifold. This matrix regularization is given as a natural generalization of the Berezin–Toeplitz quantization and gives a map from sections of a vector bundle to matrices. We examine the asymptotic behaviors of the map in the large-Nlimit. For vector bundles with algebraic structure, we derive a beautiful correspondence of the algebra of sections and the algebra of corresponding matrices in the large-Nlimit. We give two explicit examples for monopole bundles over a complex projective spaceCPnand a torusT2n.