On S-duality and Gauss reciprocity law

Abstract

We review the interpretation of Tate's thesis by a sort of conformal field theory on a number field in \cite{1}. Based on this and the existence of a hypothetical 3-dimensional gauge theory, we give a physical interpretation of the Gauss quadratic reciprocity law by a sort of S-duality.

Some concepts are clarified, some typos are corrected