The fate of boundary terms in dimensional reductions

TL;DR

This paper investigates how Gibbons-Hawking-York boundary terms behave under dimensional reduction in various gravitational theories, providing a consistent method to derive boundary terms for higher-derivative gravity models.

Contribution

It demonstrates that GHY terms in higher-dimensional theories correctly reduce to boundary terms in lower dimensions, including for higher-derivative gravity models, offering a new way to generate such terms.

Findings

GHY terms reduce consistently across dimensions

Derived novel boundary terms for higher-derivative gravities

Established a method for generating boundary terms in complex theories

Abstract

Gibbons-Hawking-York (GHY) terms are typically neglected when performing dimensional reductions of gravitational theories. We consider the reduction of such terms for both two-derivative and four-derivative theories in general dimensions. We demonstrate a robust consistency wherein the GHY term in the original, higher-dimensional theory translates directly to the appropriate GHY term in the dimensionally reduced theory. In particular, this gives a novel way of generating such terms for higher-derivative corrections. We carry out this procedure for Gauss-Bonnet, Chern-Simons modified, and $f(R)$ gravities to derive novel boundary terms.