Exact Diffeomorphism in Warped Space

TL;DR

This paper investigates the role of exact diffeomorphism symmetry in warped extra-dimensional models, especially the Randall-Sundrum setup, revealing how it influences radion stabilization and mass protection.

Contribution

It derives nonlinear transformation rules for metric fields and shows how on-shell diffeomorphism symmetry affects radion mass and stabilization mechanisms.

Findings

On-shell diffeomorphism exists before radion stabilization

Goldberger-Wise mechanism breaks on-shell diffeomorphism

Diffeomorphism symmetry may protect radion from acquiring mass

Abstract

In this paper, we study the manifestation of exact diffeomorphism in warped extra dimension, with an emphasis on the Randall-Sundrum model. Utilizing the covariant form of variation $\delta g_{MN} = \nabla_M \xi_N + \nabla_N \xi_M$, we derive the nonlinear transformation rules for the metric fields in the unitary gauge. As an off-shell symmetry, diffeomorphism governs the interaction structure by connecting the neighboring orders of bulk action expansions. Our analysis unveils that an on-shell diffeomorphism exists prior to radion stabilization, but is broken by the Goldberger-Wise mechanism. This on-shell symmetry enforces a mass-related equation $F'- A' G =0$ to eliminate one degree of freedom, while ensuring the 5D action invariant up to a surface term. Therefore, we conjecture that the on-shell diffeomorphism actually protects the radion field from acquiring mass.