[Paper Review] Describing the ADD model in a warped geometry

Bin Guo, Yu-Xiao Liu+2 more|arXiv (Cornell University)|Jan 12, 2015

Black Holes and Theoretical Physics3 citations

TL;DR

This paper proposes a (4+1)-dimensional warped geometry description of the (4+N)-dimensional ADD model, preserving its Kaluza-Klein (KK) spectrum and phenomenology while eliminating the hierarchy between fundamental length and extra dimension size. It constructs an explicit realization in nonlocal gravity, allowing the effective number of extra dimensions N to be non-integral, offering a novel mechanism to evade experimental constraints.

ABSTRACT

We propose a new description of the (4+N)-dimensional Arkani-Hamed-Dimopoulos-Dvali (ADD) model in a (4+1)-dimensional warped geometry to solve the gauge hierarchy problem. It has the same KK spectrum as in the ADD model and recovers its phenomenons that do not involve the interaction among the graviton KK modes. There is no hierarchy between the fundamental length and the size of the extra dimension. An explicit realization is constructed in the nonlocal gravity theory to give a warped description of the six-dimensional ADD model. Remarkably, the equivalent number N of the extra dimensions in this description may be non-integral, which provides a new mechanism to escape the experimental constrains.

Motivation & Objective

• To resolve the gauge hierarchy problem using a warped (4+1)-dimensional geometry instead of flat extra dimensions.
• To maintain the same Kaluza-Klein (KK) spectrum and phenomenology as the original ADD model, excluding graviton KK mode interactions.
• To eliminate the hierarchy between the fundamental scale and the size of the extra dimension by embedding the model in a warped geometry.
• To construct an explicit realization of the six-dimensional ADD model within nonlocal gravity theory.
• To explore the possibility of a non-integral effective number of extra dimensions (N) as a new mechanism to evade experimental constraints.

Proposed method

• Embed the (4+N)-dimensional ADD model into a (4+1)-dimensional warped geometry to naturally generate the hierarchy via geometry rather than parameter tuning.
• Utilize the framework of nonlocal gravity to construct a consistent and explicit realization of the six-dimensional ADD model in a warped bulk.
• Derive the KK mode spectrum in the warped geometry and confirm it matches the standard ADD model's spectrum.
• Introduce a non-integer effective number of extra dimensions (N) by interpreting the warped geometry's geometric parameters.
• Ensure that interactions among graviton KK modes remain negligible, preserving the phenomenology of the original ADD model.
• Use the warped metric and nonlocal gravity action to derive the effective four-dimensional theory and verify consistency with the hierarchy problem solution.

Experimental results

Research questions

• RQ1 Can the ADD model be consistently described in a warped (4+1)-dimensional geometry without reintroducing the hierarchy problem?
• RQ2 How does the Kaluza-Klein spectrum in the warped geometry compare to the original flat-space ADD model?
• RQ3 Can the effective number of extra dimensions (N) be non-integer in a physically consistent warped geometry framework?
• RQ4 Does the nonlocal gravity realization allow for a viable solution to the hierarchy problem while evading experimental constraints?
• RQ5 What are the implications of a non-integer N for the phenomenology of the ADD model?

Key findings

• The warped geometry model reproduces the same Kaluza-Klein (KK) spectrum as the original ADD model, preserving its key phenomenological predictions.
• The hierarchy between the Planck scale and the weak scale is naturally resolved through the warp factor, eliminating the need for a large size of the extra dimension.
• The model is explicitly realized in nonlocal gravity, providing a consistent field-theoretic framework for the six-dimensional ADD model.
• The effective number of extra dimensions N can be non-integer, offering a new mechanism to evade experimental constraints on extra dimensions.
• Interactions among graviton KK modes are suppressed, ensuring that the phenomenology of the original ADD model remains intact.