Vector bundles on fuzzy Kähler manifolds

Abstract 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-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 CPn and a torus T2n.