[Paper Review] `Desert' in Energy or Transverse Space?

Constantin P. Bachas|ArXiv.org|Jul 5, 1999

Global Energy and Sustainability Research3 citations

TL;DR

This paper explores the Brane World scenario as an alternative to the conventional 'energy desert' in particle physics, proposing that a hierarchically large extra dimension (transverse space) can replace the gap between the electroweak and Planck scales. By embedding our 3+1-dimensional universe on a brane in a higher-dimensional bulk, the theory avoids the hierarchy problem without requiring new physics at the weak scale, offering a novel mechanism for electroweak unification.

ABSTRACT

I review the issue of string and compactification scales in the weak-coupling regimes of string theory. I explain how in the Brane World scenario a (effectively) two-dimensional transverse space that is hierarchically larger than the string length may replace the conventional `energy desert' described by renormalizable supersymmetric QFT. I comment on the puzzle of unification in this context.

Motivation & Objective

• To re-express the hierarchy problem in string theory and compactification scales beyond conventional field theory.
• To investigate whether a large transverse extra dimension can replace the standard 'energy desert' in the renormalizable supersymmetric quantum field theory framework.
• To analyze the implications of this alternative for electroweak unification and the scale of new physics.
• To assess the viability of the Brane World scenario in resolving the hierarchy problem without new physics at the weak scale.

Proposed method

• Analyzes weak-coupling regimes of string theory to identify effective field theory descriptions.
• Applies the framework of brane-world cosmology, where our universe is a 3-brane embedded in a higher-dimensional bulk.
• Considers the role of compactification scales and the size of the transverse extra dimension relative to the string length.
• Uses effective field theory techniques to derive low-energy phenomenology from higher-dimensional gravity and gauge theories.
• Compares the energy scale gap (the 'desert') in standard model with the geometric hierarchy in transverse space.
• Evaluates consistency with electroweak unification and the absence of new physics at the weak scale.

Experimental results

Research questions

• RQ1 Can a large transverse extra dimension replace the conventional energy desert in the hierarchy problem?
• RQ2 How does the Brane World scenario modify the standard picture of electroweak unification?
• RQ3 What are the implications of a hierarchically large extra dimension for the scale of quantum gravity and unification?
• RQ4 How does the weak-coupling regime of string theory support or constrain this geometric resolution of the hierarchy problem?
• RQ5 Can the absence of new physics at the weak scale be naturally explained by a large transverse space rather than by supersymmetry?

Key findings

• The paper proposes that the conventional energy desert between the electroweak and Planck scales can be replaced by a geometric hierarchy in transverse space, where the extra dimension is much larger than the string scale.
• In the Brane World scenario, the hierarchy problem is resolved not by new physics at the weak scale, but by the large size of the transverse dimension.
• The effective four-dimensional Planck scale is generated by the volume of the extra dimension, providing a natural explanation for the hierarchy.
• The model avoids the need for fine-tuning in the Higgs sector by separating the scales geometrically rather than dynamically.
• Electroweak unification remains viable in this framework, though the unification scale may be shifted due to the modified Kaluza-Klein spectrum.
• The analysis suggests that the absence of new physics at the weak scale may be a consequence of the large transverse dimension rather than a sign of missing dynamics.