Abelian Chern-Simons term as a Kaluza-Klein dimensional reduction of the Gibbons-Hawking surface term

Abstract

It is suggested that the original, minimal Kaluza-Klein theory should be extended by adding a 5-dimensional version of the Gibbons-Hawking gravitational surface term. It is then demonstrated that the usual dimensional reduction of the newly added surface (boundary) term leads to the emergence of the famous Abelian Chern-Simons term. It is stressed that the advent of this Chern-Simons term is not merely a parametrization artefact but a real thing. Finally, the issue of finite-ranged electromagnetic interaction due to massive photons on a plane has been interpreted in terms of the violation of the local gauge invariance of this extended version of Kaluza-Klein theory.