RandallSundrum

Randall-Sundrum refers to a pair of related theoretical models proposed by Lisa Randall and Raman Sundrum in 1999 to address the hierarchy problem through a warped extra dimension. The core idea is a five-dimensional spacetime with a non-factorizable geometry, specifically an anti-de Sitter (AdS5) bulk, bounded by one or two 3-branes. The two main versions are known as RS1 and RS2, each with distinct phenomenology and implications.

RS1 posits a finite extra dimension bounded by two 3-branes: a Planck brane and a TeV brane. The five-dimensional metric contains a warp factor that redshifts mass scales along the extra dimension, so that a Planck-scale mass on the Planck brane appears at the TeV scale on the TeV brane. With an appropriate compactification radius, the large hierarchy between the Planck and weak scales is generated without large input parameters. Stabilization of the brane separation is necessary and is commonly addressed by mechanisms such as Goldberger-Wise.

RS2 replaces the second brane with an infinite extra dimension, preserving a single brane. The AdS warp factor localizes gravity near the brane, yielding effective four-dimensional gravity at observable distances, while a continuum of Kaluza-Klein graviton modes modifies gravity at short ranges or high energies.

Impact and legacy: the Randall-Sundrum framework popularized warped extra dimensions and braneworld scenarios, influencing approaches to holography and beyond-Standard Model phenomenology. Experimental constraints from collider searches and precision gravity tests have limited certain parameter regions, but variants with Standard Model fields in the bulk continue to be explored.