[Paper Review] TASI Lectures on Extra Dimensions and Branes

Csaba Csáki|ArXiv.org|Apr 9, 2004

Black Holes and Theoretical Physics138 references115 citations

TL;DR

This paper provides a pedagogical introduction to theories with branes and extra dimensions, focusing on large and warped extra dimensions. It explains how to construct effective field theories on branes, derives Kaluza-Klein phenomenology, and details the Randall-Sundrum model’s solution to the hierarchy problem via warped geometry and gravity localization, with key results on gauge coupling matching and custodial symmetry protection in composite Higgs models.

ABSTRACT

This is a pedagogical introduction into theories with branes and extra dimensions. We first discuss the construction of such models from an effective field theory point of view, and then discuss large extra dimensions and some of their phenomenological consequences. Various possible phenomena (split fermions, mediation of supersymmetry breaking and orbifold breaking of symmetries) are discussed next. The second half of this review is entirely devoted to warped extra dimensions, including the construction of the Randall-Sundrum solution, intersecting branes, radius stabilization, KK phenomenology and bulk gauge bosons.

Motivation & Objective

• To provide a pedagogical foundation for researchers entering the field of extra dimensions and brane-world models.
• To explain how brane-localized fields and Kaluza-Kinkle modes emerge from higher-dimensional effective field theories.
• To explore the phenomenological implications of large extra dimensions, including TeV-scale gravity and black hole production.
• To detail the Randall-Sundrum mechanism as a solution to the hierarchy problem using warped geometry and brane-localized gravity.
• To connect the RS model to the AdS/CFT correspondence and discuss its implications for composite Higgs and gauge coupling running.

Proposed method

• Derives the effective 4D Lagrangian for brane-localized fields in higher-dimensional spacetime using Kaluza-Klein compactification.
• Applies orbifold projections to break gauge symmetries and break supersymmetry, enabling model-building with chiral fermions.
• Constructs the Randall-Sundrum solution by solving Einstein's equations in 5D with a negative cosmological constant and two branes.
• Analyzes gravity localization via the warp factor $e^{-k|y|}$, showing zero-mode wavefunction localization on the TeV brane.
• Computes the Kaluza-Klein graviton spectrum and coupling to SM fields, including the $g_4^2 = g_5^2 / (R \log(R'/R))$ matching relation.
• Uses the AdS/CFT correspondence to interpret the RS model as a walking technicolor theory with a composite Higgs, and introduces custodial symmetry restoration via bulk $SU(2)_R$ gauge fields.

Experimental results

Research questions

• RQ1 How can extra dimensions be hidden from low-energy experiments while still producing observable effects?
• RQ2 What is the mechanism by which the hierarchy problem is solved in the Randall-Sundrum model with warped extra dimensions?
• RQ3 How do bulk gauge fields and fermions in the 5D bulk lead to realistic 4D gauge couplings and fermion masses?
• RQ4 What is the role of orbifolds in breaking gauge symmetries and supersymmetry in flat extra dimension models?
• RQ5 How does the AdS/CFT correspondence relate the RS model to strongly coupled conformal field theories and composite Higgs phenomenology?

Key findings

• The Randall-Sundrum model solves the hierarchy problem via exponential warping of the extra dimension, localizing the graviton zero mode on the TeV brane.
• The matching relation $g_4^2 = g_5^2 / (R \log(R'/R))$ shows that 5D gauge coupling runs logarithmically in the 4D effective theory due to CFT modes in the bulk.
• Custodial symmetry is restored in the RS model by introducing $SU(2)_R$ gauge fields in the bulk and breaking $SU(2)_R$ on the Planck brane to eliminate its zero mode.
• The RS model can be interpreted as a walking technicolor model with a composite Higgs, where electroweak symmetry breaking arises from strong dynamics in the CFT.
• Bulk gauge fields in the RS model lead to a modified Higgs mass and corrections to $W$ and $Z$ boson masses, which are tamed by custodial symmetry.
• The model predicts a tower of Kaluza-Klein gravitons with masses $m_n \sim k \cdot (n + 1/2)$, with couplings to SM fields suppressed by the warp factor.