Gravitational Higgs Mechanism

TL;DR

This paper explores the gravitational Higgs mechanism in 5D domain wall backgrounds, analyzing fluctuations, normalizability, and matter coupling, revealing differences from Randall-Sundrum models and quantum inconsistencies.

Contribution

It provides a detailed analysis of gravitational fluctuations and matter coupling in domain wall backgrounds, highlighting differences from Randall-Sundrum models and quantum issues.

Findings

Scalar and graviphoton fluctuations can be gauged away.

Graviton zero mode is quadratically normalizable.

Coupling to matter is consistent only if matter is conformal.

Abstract

We discuss the gravitational Higgs mechanism in domain wall background solutions that arise in the theory of 5-dimensional Einstein-Hilbert gravity coupled to a scalar field with a non-trivial potential. The scalar fluctuations in such backgrounds can be completely gauged away, and so can be the graviphoton fluctuations. On the other hand, we show that the graviscalar fluctuations do not have normalizable modes. As to the 4-dimensional graviton fluctuations, in the case where the volume of the transverse dimension is finite the massive modes are plane-wave normalizable, while the zero mode is quadratically normalizable. We then discuss the coupling of domain wall gravity to localized 4-dimensional matter. In particular, we point out that this coupling is consistent only if the matter is conformal. This is different from the Randall-Sundrum case as there is a discontinuity in the delta-function-like limit of such a smooth domain wall - the latter breaks diffeomorphisms only spontaneously, while the Randall-Sundrum brane breaks diffeomorphisms explicitly. Finally, at the quantum level both the domain wall as well as the Randall-Sundrum setups suffer from inconsistencies in the coupling between gravity and localized matter, as well as the fact that gravity is generically expected to be delocalized in such backgrounds due to higher curvature terms.