[Paper Review] On Relation between Two Models of Gauge Field Localization on a Brane

Motoi Tachibana|ArXiv.org|Aug 22, 2001

Black Holes and Theoretical Physics13 references3 citations

TL;DR

This paper establishes a direct relationship between two distinct models of gauge field localization on a brane in the Randall-Sundrum model: one using bulk and boundary mass terms, and another using a gauge field-dilaton coupling. Through a field redefinition, it is shown that the dilaton-coupled model can be transformed into a form equivalent to the massive gauge theory model, revealing that the boundary mass term arises naturally from the orbifold geometry, with consistent parameter relations under the hierarchy problem constraints.

ABSTRACT

We discuss the relation between two different models which are recently proposed as the model of localizing bulk gauge fields on a brane. In the former model, the localization of gauge field is achieved by adding both bulk and boundary mass terms while in the latter, it is done by taking into consideration the coupling between the gauge field and the dilaton field (this model is also regarded as the gauge theory with nontrivial dielectric ``constant''). We make a certain transformation for the gauge field in the latter Lagrangian. As the result, we find those two models are closely related to each other.

Motivation & Objective

• To investigate the theoretical relationship between two recently proposed models of gauge field localization on a brane in the Randall-Sundrum model.
• To determine whether the model with bulk and boundary mass terms is physically equivalent to the model with gauge field-dilaton coupling.
• To clarify the origin of the boundary mass term in the context of orbifold compactification.
• To derive consistent parameter relations between the two models under the requirement of solving the hierarchy problem.

Proposed method

• A field redefinition is applied to the gauge field in the dilaton-coupled model, transforming it into a form resembling the massive gauge theory model.
• The transformation is based on the conjecture that the exponential of the dilaton field acts as an effective dielectric constant.
• The action is expanded in the brane limit (a → ∞) with fixed ξ = 3βa, leading to a step-function behavior for the scalar fields.
• The resulting action is compared to the massive model Lagrangian, revealing matching kinetic and mass terms.
• Partial integration is used to convert a mixed derivative term into a boundary mass term proportional to δ(y).
• Parameter matching is performed between the two models, showing equivalence in bulk and boundary mass relations.

Experimental results

Research questions

• RQ1 Can the gauge field localization mechanism via dilaton coupling be mapped to the mechanism using explicit bulk and boundary mass terms?
• RQ2 What is the origin of the boundary mass term in the dilaton-coupled model?
• RQ3 How do the parameters in the two models relate under the physical requirement of solving the hierarchy problem?
• RQ4 Is the field redefinition proposed in the paper sufficient to establish equivalence between the two models?

Key findings

• The dilaton-coupled model can be transformed into a form identical to the massive gauge theory model via a field redefinition, establishing a close physical equivalence.
• The boundary mass term in the massive model arises from the orbifold geometry and the discontinuity in the dilaton field's derivative at y = 0.
• The bulk mass parameter M′ in the dilaton model is related to the boundary mass c′ by M′ ≈ |c′|, matching the relation M²L ≈ |c| in the massive model.
• The parameter c′ in the dilaton model is found to be c′ = -2λξ²/3, indicating a tachyonic mass term on the brane if λ > 0.
• The relation M′² = λ²ξ⁴/36 and c′ = -2λξ²/3 ensures consistency with the hierarchy problem requirement that M ≈ M_Pl and |c| ≈ M.
• The physical origin of the boundary mass is traced to the discontinuity in the derivative of the effective dielectric function ε(π) at the brane.