Gerbes in Renormalization and Quantization of Infinite-Dimensional Moduli Spaces

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Renormalization is a fundamental problem in the study of infinite-dimensional moduli spaces in order to extract meaningful quantities from these. In the considered cases (Yang-Mills theory, holomorphic curves) zeta regularization allows the construction of the Quillen metric on the determinant line bundle. The present project sketches an alternative approach to these metrics, which in the case of holomorphic curves are then compared to recent advances in the theory of elliptic genera.