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\section*{Randall-Sundrum model}

\hypertarget{context}{}\subsubsection*{{Context}}\label{context}

\hypertarget{gravity}{}\paragraph*{{Gravity}}\label{gravity}

[[!include gravity contents]]

\hypertarget{string_theory}{}\paragraph*{{String theory}}\label{string_theory}

[[!include string theory - contents]]

\hypertarget{contents}{}\section*{{Contents}}\label{contents}

\noindent\hyperlink{idea}{Idea}\dotfill \pageref*{idea} \linebreak
\noindent\hyperlink{related_concepts}{Related concepts}\dotfill \pageref*{related_concepts} \linebreak
\noindent\hyperlink{references}{References}\dotfill \pageref*{references} \linebreak
\noindent\hyperlink{general}{General}\dotfill \pageref*{general} \linebreak
\noindent\hyperlink{as_intersecting_brane_models_in_string_theory}{As intersecting brane models in string theory}\dotfill \pageref*{as_intersecting_brane_models_in_string_theory} \linebreak
\noindent\hyperlink{cosmology}{Cosmology}\dotfill \pageref*{cosmology} \linebreak
\noindent\hyperlink{in_gaugehiggs_grand_unification}{In gauge-Higgs grand unification}\dotfill \pageref*{in_gaugehiggs_grand_unification} \linebreak
\noindent\hyperlink{observation}{Observation}\dotfill \pageref*{observation} \linebreak


\hypertarget{idea}{}\subsection*{{Idea}}\label{idea}

The \emph{Randall-Sumdrum model} (\hyperlink{RandallSundrum99a}{Randall-Sundrum 99a}, \hyperlink{RandallSundrum99b}{99b}) is a class of [[string theory inspired model|string theory inspired]] [[model (physics)|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 spacetime|anti de sitter]] ``[[bulk]]'' [[spacetime]], but the [[gauge fields]] and [[fermion field|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 geometry|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 \emph{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]] [[intersection|intersected]] to a 3+1-dimensional subspace. By the general lore of [[black holes in string theory]], [[non-perturbative effect|non-perturbatively]] these [[D6-branes]] are [[black branes]] with [[anti de Sitter spacetime|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 \hyperlink{Teraguchi07}{Teraguchi 07, around slide 21}, for review and further pointers see \hyperlink{Uranga02}{Uranga 02, section 18}.

For more on this see at \emph{[[intersecting D-brane models]]} the section \emph{\href{intersecting+D-brane+model#Cosmology}{Cosmology and Holography}}.

\hypertarget{related_concepts}{}\subsection*{{Related concepts}}\label{related_concepts}

\begin{itemize}%
\item [[anti de Sitter gravity]]


\item [[AdS-CFT duality]]


\item [[intersecting D-brane model]]


\item [[ekpyrotic cosmology]]


\item [[standard model of cosmology]]



\end{itemize}
\hypertarget{references}{}\subsection*{{References}}\label{references}

\hypertarget{general}{}\subsubsection*{{General}}\label{general}

The model was introduced in

\begin{itemize}%
\item Lisa Randall, Raman Sundrum, \emph{A Large Mass Hierarchy from a Small Extra Dimension}, Phys.Rev.Lett.83:3370-3373, 1999 (\href{https://arxiv.org/abs/hep-ph/9905221}{arXiv:hep-ph/9905221})


\item Lisa Randall, Raman Sundrum, \emph{An Alternative to Compactification}, Phys.Rev.Lett.83:4690-4693,1999 (\href{https://arxiv.org/abs/hep-th/9906064}{arXiv:hep-th/9906064})



\end{itemize}
Different but similar approaches are

\begin{itemize}%
\item Nima Arkani-Hamed, Savas Dimopoulos, Gia Dvali, \emph{The Hierarchy Problem and New Dimensions at a Millimeter}, Phys.Lett.B429:263-272,1998 (\href{https://arxiv.org/abs/hep-ph/9803315}{arXiv:hep-ph/9803315})

\end{itemize}
and the GRS model, due to

\begin{itemize}%
\item Ruth Gregory, Valery A. Rubakov, Sergei M. Sibiryakov, \emph{Opening up extra dimensions at ultra-large scales}, Phys.Rev.Lett. 84 (2000) 5928-5931 (\href{https://arxiv.org/abs/hep-th/0002072}{arXiv:hep-th/0002072})


\item Csaba Csaki, Joshua Erlich, Timothy J. Hollowood, \emph{Quasi-Localization of Gravity by Resonant Modes}, Phys. Rev. Lett.84:5932-5935, 2000 (\href{https://arxiv.org/abs/hep-th/0002161}{arXiv:hep-th/0002161})



\end{itemize}
a well as [[intersecting D-brane models]].

Review includes

\begin{itemize}%
\item Yoonbai Kim, Chong Oh Lee, Ilbong Lee, JungJai Lee, \emph{Brane World of Warp Geometry: An Introductory Review}, J. Kor. Astron. Soc. 37 (2004) 1-14 (\href{https://arxiv.org/abs/hep-th/0307023}{arXiv:hep-th/0307023})

\end{itemize}
Possible relation to [[flavour anomalies]] via potential [[leptoquarks]]:

\begin{itemize}%
\item [[Andreas Crivellin]], \emph{Explaining the Flavour Anomalies with the Pati-Salam Vector Leptoquark}, PoS LHCP2018 (2018) 269 (\href{http://inspirehep.net/record/1713260}{spire:1713260}, \href{https://doi.org/10.22323/1.321.0269}{doi:10.22323/1.321.0269})


\item Monika Blanke, [[Andreas Crivellin]], \emph{$B$ Meson Anomalies in a Pati-Salam Model within the Randall-Sundrum Background}, Phys. Rev. Lett. 121, 011801 (2018) (\href{https://arxiv.org/abs/1801.07256}{arXiv:1801.07256})



\end{itemize}
\hypertarget{as_intersecting_brane_models_in_string_theory}{}\subsubsection*{{As intersecting brane models in string theory}}\label{as_intersecting_brane_models_in_string_theory}

Discussion of relation to [[string theory]] originates around

\begin{itemize}%
\item [[Edward Witten]], from p. 8 on in \emph{The Cosmological Constant From The Viewpoint Of String Theory}, in \emph{Sources and detection of dark matter and dark energy in the universe}, Springer 2001. 27-36. (\href{https://arxiv.org/abs/hep-ph/0002297}{arXiv:hep-ph/0002297})


\item [[Steven Giddings]], [[Shamit Kachru]], [[Joseph Polchinski]], \emph{Hierarchies from Fluxes in String Compactifications}, Phys. Rev. D66:106006, 2002 (\href{https://arxiv.org/abs/hep-th/0105097}{arXiv:hep-th/0105097})



\end{itemize}
Review of the relation to [[string theory]]/[[intersecting D-brane models]] includes

\begin{itemize}%
\item [[Angel Uranga]], section 18 of \emph{TASI lectures on String Compactification, Model Building, and Fluxes} (\href{https://arxiv.org/abs/hep-th/0201209}{arXiv:hep-th/0201209})


\item Shunsuke Teraguchi, around slide 21 \emph{String theory and its relation to particle physics}, 2007 (\href{http://phys.cts.ntu.edu.tw/ppp7/talks/PPP7_Shunsuke_Teraguchi.pdf}{pdf})



\end{itemize}
based on

\begin{itemize}%
\item [[Igor Klebanov]], [[Matthew Strassler]], \emph{Supergravity and a Confining Gauge Theory: Duality Cascades and $\chi^{SB}$-Resolution of Naked Singularities}, JHEP 0008:052, 2000 (\href{https://arxiv.org/abs/hep-th/0007191}{arXiv:hep-th/0007191})


\item [[Igor Klebanov]], [[Edward Witten]], \emph{Superconformal Field Theory on Threebranes at a Calabi-Yau Singularity}, Nucl.Phys.B536:199-218, 1998 (\href{https://arxiv.org/abs/hep-th/9807080}{arXiv:hep-th/9807080})



\end{itemize}
with further developments including

\begin{itemize}%
\item Nemanja Kaloper, \emph{Origami World}, JHEP 0405 (2004) 061 (\href{https://arxiv.org/abs/hep-th/0403208}{arXiv:hep-th/0403208})


\item Antonino Flachi, Masato Minamitsuji, \emph{Field localization on a brane intersection in anti-de Sitter spacetime}, Phys.Rev.D79:104021, 2009 (\href{https://arxiv.org/abs/0903.0133}{arXiv:0903.0133})



\end{itemize}
Relation to [[AdS-CFT duality]]:

\begin{itemize}%
\item Jiro Soda, \emph{AdS/CFT on the brane}, Lect.Notes Phys.828:235-270, 2011 (\href{https://arxiv.org/abs/1001.1011}{arXiv:1001.1011})

\end{itemize}
\hypertarget{cosmology}{}\subsubsection*{{Cosmology}}\label{cosmology}

Discussion of [[cosmology]] on branes in $\sim$ [[anti de Sitter spacetime|anti de Sitter]]-[[near horizon geometry|throat]] geometries:

\begin{itemize}%
\item Tetsuya Shiromizu, Daisuke Ida, \emph{Anti-de Sitter no-hair, AdS/CFT and the brane-world}, Phys. Rev. D64 (2001) 044015 (\href{https://arxiv.org/abs/hep-th/0102035}{arXiv:hep-th/0102035})


\item Antonio Padilla, \emph{Braneworld Cosmology and Holography} (\href{https://arxiv.org/abs/hep-th/0210217}{arxiv:hep-th/0210217})



\end{itemize}
On [[de Sitter spacetime]] [[cosmology]] realized in [[brane world models]] in ambient $\sim$[[anti de Sitter spacetime|AdS]]-[[bulk]] [[spacetime]]:

\begin{itemize}%
\item Souvik Banerjee, [[Ulf Danielsson]], Giuseppe Dibitetto, Suvendu Giri, Marjorie Schillo, \emph{Emergent de Sitter cosmology from decaying AdS} (\href{https://arxiv.org/abs/1807.01570}{arXiv:1807.01570})


\item Souvik Banerjee, [[Ulf Danielsson]], Giuseppe Dibitetto, Suvendu Giri, Marjorie Schillo, \emph{de Sitter Cosmology on an expanding bubble} (\href{https://arxiv.org/abs/1907.04268}{arXiv:1907.04268})



\end{itemize}
\hypertarget{in_gaugehiggs_grand_unification}{}\subsubsection*{{In gauge-Higgs grand unification}}\label{in_gaugehiggs_grand_unification}

RS-like models for [[gauge-Higgs unification|gauge-Higgs]] [[grand unified theories]]:

with [[Spin(11)]] (``[[SO(11)]]'') [[gauge group]]:

\begin{itemize}%
\item [[Yutaka Hosotani]], Naoki Yamatsu, \emph{Gauge–Higgs grand unification}, Progress of Theoretical and Experimental Physics, Volume 2015, Issue 11, November 2015 (\href{https://doi.org/10.1093/ptep/ptv153}{doi:10.1093/ptep/ptv153}, \href{https://doi.org/10.1093/ptep/ptw116}{doi:10.1093/ptep/ptw116})


\item Atsushi Furui, [[Yutaka Hosotani]], Naoki Yamatsu, \emph{Toward Realistic Gauge-Higgs Grand Unification}, Progress of Theoretical and Experimental Physics, Volume 2016, Issue 9, September 2016, 093B01 (\href{https://arxiv.org/abs/1606.07222}{arXiv:1606.07222})


\item [[Yutaka Hosotani]], \emph{New dimensions from gauge-Higgs unification} (\href{https://arxiv.org/abs/1702.08161}{arXiv:1702.08161})


\item [[Yutaka Hosotani]], Naoki Yamatsu, \emph{Electroweak Symmetry Breaking and Mass Spectra in Six-Dimensional Gauge-Higgs Grand Unification} (\href{https://arxiv.org/abs/1710.04811}{arXiv:1710.04811})



\end{itemize}
with [[Spin(12)]] (``[[SO(12)]]'') [[gauge group]]:

\begin{itemize}%
\item S. Rajpoot and P. Sithikong, \emph{Implications of the $SO(12)$ gauge symmetry for grand unification}, Phys. Rev. D 23, 1649 (1981) (\href{https://doi.org/10.1103/PhysRevD.23.1649}{doi:10.1103/PhysRevD.23.1649})


\item Takaaki Nomura and Joe Sato, \emph{Standard(-like) Model from an $SO(12)$ Grand Unified Theory in six-dimensions with $S^2$ extra-space}, Nucl.Phys.B811:109-122, 2009 (\href{https://arxiv.org/abs/0810.0898}{arXiv:0810.0898})


\item Takaaki Nomura, \emph{Physics beyond the standard model with $S^2$ extra-space}, 2009 (\href{http://krishna.th.phy.saitama-u.ac.jp/joe/doctor/nomura-doctor.pdf}{pdf}, [[NomuraSO12GUT.pdf:file]])


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



\end{itemize}
\hypertarget{observation}{}\subsubsection*{{Observation}}\label{observation}

\begin{itemize}%
\item Indrani Banerjee, Sumanta Chakraborty, Soumitra SenGupta, \emph{Silhouette of M87${}^*$: A new window to peek into the world of hidden dimensions} (\href{https://arxiv.org/abs/1909.09385}{arXiv:1909.09385})

\end{itemize}
[[!redirects Randall-Sundrum models]]

[[!redirects RS model]] [[!redirects RS models]] [[!redirects RS-model]] [[!redirects RS-models]]

[[!redirects GRS model]] [[!redirects GRS models]] [[!redirects GRS-model]] [[!redirects GRS-models]]



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