Randall–Sundrum

Randall–Sundrum is a pair of influential models in high-energy theoretical physics proposing warped extra dimensions to address the hierarchy between the electroweak scale and the Planck scale. Developed in 1999 by Lisa Randall and Raman Sundrum, the models have shaped research across string theory, brane cosmology, and particle physics phenomenology, informing investigations at facilities such as the Large Hadron Collider and guiding connections to AdS/CFT correspondence and holography.

Background and motivation

The original motivation arose from attempts to reconcile the large disparity between the Planck scale and the electroweak scale highlighted in studies by practitioners at institutions including CERN and Fermilab. Influences include prior proposals such as the Kaluza–Klein theory, the ADD model by Arkani-Hamed, Dimopoulos, and Dvali, and developments in supergravity and M-theory explored at Caltech and Cambridge University. Randall and Sundrum leveraged perspectives from research on the cosmological constant problem, the hierarchy problem (physics), and the behavior of graviton modes in scenarios discussed in seminars at Princeton University and Harvard University.

Randall–Sundrum models (RS1 and RS2)

The two canonical constructions, often referenced in literature from SLAC National Accelerator Laboratory and DESY, are denoted RS1 and RS2. RS1 posits a finite extra dimension bounded by two branes, inspired by earlier work on orbifolds and domain walls in papers circulated through arXiv and presented at conferences such as Strings Conference and Moriond. RS2 retains a single brane with a non-compact extra dimension, connecting to analyses of localized gravity by researchers at Institute for Advanced Study and reported in reviews at KITP. Both models employ warped metrics analogous to metrics studied in Anti-de Sitter space and are frequently contrasted with compactification schemes used in Type IIB string theory and studies at Imperial College London.

Mathematical formulation and solutions

The models use a five-dimensional spacetime with a negative cosmological constant, drawing on mathematical structures from Anti-de Sitter space, Randall–Sundrum metric, and the formalism developed in works associated with Edward Witten and Juan Maldacena. Solutions involve solving Einstein equations with brane-localized stress-energy, techniques shared with analyses in ADM formalism, Israel junction conditions, and computations featured in papers from MIT and Yale University. Mode decomposition yields a zero-mode graviton and a discrete or continuous Kaluza–Klein tower, comparisons often made with spectra analyzed by groups at Perimeter Institute and in lectures at NORDITA. The mathematical treatment connects to boundary conditions studied in Gibbons–Hawking–York boundary term literature and to renormalization group interpretations found in AdS/CFT correspondence discussions by authors affiliated with Princeton University and Rutgers University.

Phenomenology and experimental constraints

Phenomenological implications were explored for collider signatures, precision tests, and astrophysical observations by collaborations such as ATLAS, CMS, and analysis groups at Tevatron. Constraints arise from searches for Kaluza–Klein gravitons, modifications to Newtonian gravity tested by experiments at Eöt-Wash, and consistency checks with cosmological probes including data from Planck (spacecraft) and WMAP. Limits on model parameters reference results reported at meetings like ICHEP and in review articles distributed through arXiv by researchers at University of Chicago and University of California, Berkeley. Proposed signals such as narrow graviton resonances and deviations in electroweak precision observables were central to studies by teams at Brookhaven National Laboratory and Lawrence Berkeley National Laboratory.

Extensions and related theories

Extensions build bridges to string theory compactifications, gauge/gravity duality, and warped throat constructions explored by groups at Stanford University and University of Cambridge. Variants incorporate supersymmetry as in work influenced by Nima Arkani-Hamed and Savas Dimopoulos, or embed RS setups into heterotic string theory and F-theory frameworks studied at Rutgers University and University of Oxford. Related lines of inquiry include deformations addressing the cosmological constant problem via mechanisms proposed in seminars at Perimeter Institute, interactions with dark matter model-building pursued by teams at University of Michigan, and holographic composite Higgs scenarios developed by researchers at NYU and Columbia University.

Category:Theoretical physics