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arXiv · 2407.06086

Exact Diffeomorphism in Warped Space

Haiying Cai
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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 $δg_{MN} = \nabla_M ξ_N + \nabla_N ξ_M$, 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.

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Haiying Cai. 2024-07-08. Exact Diffeomorphism in Warped Space. https://arxiv.org/abs/2407.06086

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