Gerbes in Renormalization and Quantization of Infinite-Dimensional Moduli Spaces

为了从无限维模空间中提取有意义的量，重整化是研究无限维模空间的一个基本问题。在考虑的情况下（Yang-Mills理论，全纯曲线），zeta正则化允许在行列式线束上构造Quillen度规。本项目概述了这些度量的另一种方法，在全纯曲线的情况下，将其与椭圆属理论的最新进展进行比较。

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.