Abelian Chern-Simons theory on the torus and physical views on the Hecke operators

Abstract

In the previous paper arXiv:1711.07122, we show that a holomorphic zero-mode wave function in abelian Chern-Simons theory on the torus can be considered as a quantum version of a modular form of weight 2. Motivated by this result, in this paper we consider an action of a Hecke operator on such a wave function from a gauge theoretic perspective. This leads us to obtain some physical views on the Hecke operators in number theory.

19 pages. arXiv admin note: text overlap with arXiv:1711.07122

References in corpus (3)

• Elements of Geometric Quantization and Applications to Fields and Fluids
• Analogies between Knots and Primes, 3-Manifolds and Number Rings
• Some properties of zero-mode wave functions in abelian Chern-Simons theory on the torus

Cited by in corpus (1)

• Some properties of zero-mode wave functions in abelian Chern-Simons theory on the torus