November 21, 2017

Paper submitted to arXiv

In this paper we argue that in the context of geometric quantization holomorphic part of zero-mode wave function in abelian Chern-Simons theory on the torus can be considered as modular forms of weight two. Part of the arguments are made possible by imposing gauge invariance on the zero-mode wave function where gauge transformations are induced by modular transformations of the zero-mode variable.