nLab Randall-Sundrum model

Idea

The Randall-Sumdrum model (Randall-Sundrum 99a, 99b) is a class of string theory inspired models in combined cosmology and particle physics, which assume that the observable universe constitutes the asymptotic boundary of an ambient anti de Sitter spacetime: the force of gravity would pertain to the full anti de sitter “bulk” spacetime, but the gauge fields and fermion matter fields would be constrained to reside on that boundary, as would hence be all observations made via electromagnetic radiation by observers inside this cosmology.

Hence the extra bulk dimensions in these models need not be small (technically: the fiber spaces need not be compact topological spaces with tiny Riemannian volume) in order to be unobservable for observers. This is in contrast to the (historically much older) Kaluza-Klein compactification models for physics with extra dimensions. Therefore Randall-Sumdrum-like models are also referred to as large extra dimension models.

One original motivation for the RS-models was the idea that this setup could address the hierarchy problem.

Something at least close to Randall-Sundrum models naturally appears in string phenomenology: In intersecting D-brane models the standard model of particle physics is part of the worldvolume quantum field theory of D6-branes intersected to a 3+1-dimensional subspace. By the general lore of black holes in string theory, non-perturbatively these D6-branes are black branes with anti de Sitter near horizon geometry. Hence the cosmology of intersecting D-brane models is qualitatively of Randall-Sundrum form, even if details may differ. For the quick idea see Teraguchi 07, around slide 21, for review and further pointers see Uranga 02, section 18.

For more on this see at intersecting D-brane models the section Cosmology and Holography.

Related concepts

• D=5 Yang-Mills theory, D=5 Einstein-Maxwell theory

• hadron Kaluza-Klein theory, hadron supersymmetry

  • flavor brane

• anti de Sitter gravity

• AdS-CFT duality

• intersecting D-brane model

• ekpyrotic cosmology

• standard model of cosmology

References

General

The model was introduced in

• Lisa Randall, Raman Sundrum, A Large Mass Hierarchy from a Small Extra Dimension, Phys.Rev.Lett.83:3370-3373, 1999 (arXiv:hep-ph/9905221)

• Lisa Randall, Raman Sundrum, An Alternative to Compactification, Phys.Rev.Lett.83:4690-4693,1999 (arXiv:hep-th/9906064)

Different but similar approaches are

• Nima Arkani-Hamed, Savas Dimopoulos, Gia Dvali, The Hierarchy Problem and New Dimensions at a Millimeter, Phys.Lett.B429:263-272 (1998) (arXiv:hep-ph/9803315)

and the GRS model, due to

• Ruth Gregory, Valery A. Rubakov, Sergei M. Sibiryakov, Opening up extra dimensions at ultra-large scales, Phys.Rev.Lett. 84 (2000) 5928-5931 (arXiv:hep-th/0002072)

• Csaba Csaki, Joshua Erlich, Timothy J. Hollowood, Quasi-Localization of Gravity by Resonant Modes, Phys. Rev. Lett.84:5932-5935, 2000 (arXiv:hep-th/0002161)

a well as intersecting D-brane models.

More on the localized gravity in RS-models:

• Andreas Karch, Lisa Randall, Locally Localized Gravity, JHEP 0105:008 (2001) [arXiv:hep-th/0011156, doi:10.1088/1126-6708/2001/05/008]

Review:

• Yoonbai Kim, Chong Oh Lee, Ilbong Lee, JungJai Lee, Brane World of Warp Geometry: An Introductory Review, J. Kor. Astron. Soc. 37 (2004) 1-14 (arXiv:hep-th/0307023)

• André Juan Ferreira-Martins, Gravity and its wonders: braneworlds and holography (arXiv:2105.10062)

Possible relation to flavour anomalies via potential leptoquarks:

• Andreas Crivellin, Explaining the Flavour Anomalies with the Pati-Salam Vector Leptoquark, PoS LHCP2018 (2018) 269 (spire:1713260, doi:10.22323/1.321.0269)

• Monika Blanke, Andreas Crivellin, $B$ Meson Anomalies in a Pati-Salam Model within the Randall-Sundrum Background, Phys. Rev. Lett. 121, 011801 (2018) (arXiv:1801.07256)

Discussion of standard model-building in Horava-Witten-type compactifications:

• Y. H. Ahn, Sin Kyu Kang, Hyun Min Lee, Towards a Model of Quarks and Leptons (arXiv:2112.13392)

As intersecting brane models in string theory

Discussion of relation to string theory originates around

• Edward Witten, from p. 8 on in The Cosmological Constant From The Viewpoint Of String Theory, in Sources and detection of dark matter and dark energy in the universe, Springer 2001. 27-36. (arXiv:hep-ph/0002297)

• Steven Giddings, Shamit Kachru, Joseph Polchinski, Hierarchies from Fluxes in String Compactifications, Phys. Rev. D66:106006, 2002 (arXiv:hep-th/0105097)

Review of the relation to string theory/intersecting D-brane models includes

• Angel Uranga, section 18 of TASI lectures on String Compactification, Model Building, and Fluxes (arXiv:hep-th/0201209)

• Shunsuke Teraguchi, around slide 21 of: String theory and its relation to particle physics, 2007 (pdf, pdf)

based on

• Igor Klebanov, Matthew Strassler, Supergravity and a Confining Gauge Theory: Duality Cascades and $\chi^{SB}$-Resolution of Naked Singularities, JHEP 0008:052, 2000 (arXiv:hep-th/0007191)

• Igor Klebanov, Edward Witten, Superconformal Field Theory on Threebranes at a Calabi-Yau Singularity, Nucl.Phys.B536:199-218, 1998 (arXiv:hep-th/9807080)

with further developments including

• Nemanja Kaloper, Origami World, JHEP 0405 (2004) 061 (arXiv:hep-th/0403208)

• Antonino Flachi, Masato Minamitsuji, Field localization on a brane intersection in anti-de Sitter spacetime, Phys.Rev.D79:104021, 2009 (arXiv:0903.0133)

Relation to AdS-CFT duality:

• Jiro Soda, AdS/CFT on the brane, Lect.Notes Phys.828:235-270, 2011 (arXiv:1001.1011)

• Ruoyu Bao, Joseph Lykken: Randall-Sundrum with $AdS(7)$, Phys. Rev. Lett. 95 261601 (2005) [arXiv:hep-ph/0509137, doi:10.1103/PhysRevLett.95.261601]

Review and further relation to black hole entropy:

• Andreas Karch, Randall-Sundrum Branes and Holography, talk at Strings 2022 [indico:4940841]

Cosmology

Discussion of cosmology on branes in $\sim$ anti de Sitter-throat geometries:

• Tetsuya Shiromizu, Daisuke Ida, Anti-de Sitter no-hair, AdS/CFT and the brane-world, Phys. Rev. D64 (2001) 044015 (arXiv:hep-th/0102035)

• Antonio Padilla, Braneworld Cosmology and Holography (arxiv:hep-th/0210217)

On de Sitter spacetime cosmology realized in brane world models in ambient $\sim$AdS-bulk spacetime:

• Souvik Banerjee, Ulf Danielsson, Giuseppe Dibitetto, Suvendu Giri, Marjorie Schillo, Emergent de Sitter cosmology from decaying AdS (arXiv:1807.01570)

• Souvik Banerjee, Ulf Danielsson, Giuseppe Dibitetto, Suvendu Giri, Marjorie Schillo, de Sitter Cosmology on an expanding bubble (arXiv:1907.04268)

More generally on gravity on the brane:

• A. A. Zheltukhin, Brane mechanism of spontaneously generated gravity (arXiv:1912.11520)

In gauge-Higgs grand unification

RS-like models for gauge-Higgs grand unified theories:

with Spin(11) (“SO(11)”) gauge group:

• Yutaka Hosotani, Naoki Yamatsu, Gauge–Higgs grand unification, Progress of Theoretical and Experimental Physics, Volume 2015, Issue 11, November 2015 (doi:10.1093/ptep/ptv153, doi:10.1093/ptep/ptw116)

• Atsushi Furui, Yutaka Hosotani, Naoki Yamatsu, Toward Realistic Gauge-Higgs Grand Unification, Progress of Theoretical and Experimental Physics, Volume 2016, Issue 9, September 2016, 093B01 (arXiv:1606.07222)

• Yutaka Hosotani, New dimensions from gauge-Higgs unification (arXiv:1702.08161)

• Yutaka Hosotani, Naoki Yamatsu, Electroweak Symmetry Breaking and Mass Spectra in Six-Dimensional Gauge-Higgs Grand Unification (arXiv:1710.04811)

with Spin(12) (“SO(12)”) gauge group:

• S. Rajpoot and P. Sithikong, Implications of the $SO(12)$ gauge symmetry for grand unification, Phys. Rev. D 23, 1649 (1981) (doi:10.1103/PhysRevD.23.1649)

• Takaaki Nomura and Joe Sato, Standard(-like) Model from an $SO(12)$ Grand Unified Theory in six-dimensions with $S^2$ extra-space, Nucl.Phys.B811:109-122, 2009 (arXiv:0810.0898)

• Takaaki Nomura, Physics beyond the standard model with $S^2$ extra-space, 2009 (pdf, pdf)

• Cheng-Wei Chiang, Takaaki Nomura, Joe Sato, Gauge-Higgs unification models in six dimensions with $S^2/\mathbb{Z}_2$ extra space and GUT gauge symmetry (arXiv:1109.5835)

Observation

Observational hints for brane world models:

From observation of the event horizon of the black hole in the center of the galaxy Messier 87:

• Indrani Banerjee, Sumanta Chakraborty, Soumitra SenGupta, Silhouette of M87${}^*$: A new window to peek into the world of hidden dimensions (arXiv:1909.09385)

Form observation of gravitational waves from relativistic binary mergers:

• Zi-Chao Lin, Hao Yu, Yu-Xiao Liu, Constraint on the radius of five-dimensional dS spacetime with GW170817 and GRB 170817A (arXiv:2001.06581)