Gravitational Chern-Simons and the adiabatic limit

TL;DR

This paper explicitly computes the gravitational Chern-Simons term for an adiabatic family of metrics on quasi-regular K-contact manifolds, linking geometric assumptions to a Kaluza-Klein framework in general relativity.

Contribution

It introduces a novel computation of the gravitational Chern-Simons term in the adiabatic limit using K-contact geometry and Kaluza-Klein methods.

Findings

Explicit formula for the gravitational Chern-Simons term in the adiabatic limit.

Connection between K-contact geometry and Kaluza-Klein ansatz.

Extension of previous computations to the adiabatic context.

Abstract

We compute the gravitational Chern-Simons term explicitly for an adiabatic family of metrics using standard methods in general relativity. We use the fact that our base three-manifold is a quasi-regular K-contact manifold heavily in this computation. Our key observation is that this geometric assumption corresponds exactly to a Kaluza-Klein Ansatz for the metric tensor on our three manifold, which allows us to translate our problem into the language of general relativity. Similar computations have been performed in a paper of Guralnik, Iorio, Jackiw and Pi (2003), although not in the adiabatic context.