TASI Lectures on Extra Dimensions and Branes

TL;DR

The work surveys brane-world theories with extra dimensions, detailing how higher-dimensional gravity and brane-localized fields yield a 4D effective theory and distinctive phenomenology. It distinguishes flat (ADD-like) and warped (RS-like) geometries, deriving key matching relations, graviton/Kaluza-Klein spectra, and radion dynamics, and it explains how orbifold projections and brane dynamics produce chiral spectra and symmetry breaking. A central thread is the RS framework, which addresses the hierarchy problem through warping and stabilizes the radius via the Goldberger-Wise mechanism, while AdS/CFT provides a dual interpretation as a nearly conformal theory with a composite Higgs. The notes synthesize the toolkit for model-building and collider phenomenology in extra dimensions, including gravity-mediated signals, gauge fields in the bulk, and custodial symmetry constructions to align with precision data.

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.

Figures (6)

• Figure 1: Parametrization of the position of the brane in the bulk.
• Figure 2: The action of the two $Z_2$ reflections in the extended circle picture. The fundamental domain of the $S^1/Z_2$ orbifold is just the interval between $0$ and $\pi R$, and the theory can be equivalently formulated on this line segment as well.
• Figure 3: The KK towers for the various modes of the orbifold GUT theory of Hall and Nomura.
• Figure 4: The shape of the volcano potential that localizes gravity in the RS model.
• Figure 5: Intersecting branes in the RS model.