Vector bundles on fuzzy Kähler manifolds

We propose a matrix regularization of vector bundles over a general closed K\"ahler 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-\(N\) limit. 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-\(N\) limit. We give two explicit examples for monopole bundles over a complex projective space \(CP^n\) and a torus \(T^{2n}\).