Selfgravitating $SU(5)$ Higgs domain walls as a braneworlds

TL;DR

This paper investigates the stability and spectrum of self-gravitating $SU(5)$ Higgs domain walls in five dimensions, revealing the absence of tachyonic modes and the presence of massive gauge field modes, but no localizable gauge bosons.

Contribution

It provides a detailed analysis of the perturbative stability and 4D spectrum of $SU(5)$ domain walls with gravity, highlighting the non-localizability of gauge bosons and the behavior of fluctuations.

Findings

No tachyonic modes, ensuring stability.

Presence of continuous massive modes propagating in the bulk.

No localizable 4D gauge bosons, but discrete massive modes for broken directions.

Abstract

Five-dimensional domain walls in gauged $SU(5)$ generate a position-dependent symmetry breaking pattern along the additional dimension. We analize the perturbative stability and the 4D spectrum of these walls in the self-gravitating case, in terms of diffeomorphism- and Lie algebra gauge-invariant field fluctuations. We show that tachyonic modes are absent, ensuring perturbative stability. As expected, gravitational tensor and vector fluctuations behave like its counterparts in the standard $Z_2$ domain walls. All the Lie algebra valued fluctuations exhibit towers of 4D massive modes which propagate in the bulk, with a continuous spectrum starting from zero. All the would-be 4D Nambu-Goldstone fields, which are gravitationally trapped in the case of a global symmetry, are non-trivially absent. However we find no localizable 4D gauge bosons, either massless or massive. Instead, quasi-localizable discrete 4D massive modes for the gauge field fluctuations are found, along the spontaneously broken directions.