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\begin{document}

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\section*{intersecting D-brane model}

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

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

[[!include string theory - contents]]

\hypertarget{fields_and_quanta}{}\paragraph*{{Fields and quanta}}\label{fields_and_quanta}

[[!include fields and quanta - table]]

\hypertarget{quantum_field_theory}{}\paragraph*{{Quantum field theory}}\label{quantum_field_theory}

[[!include functorial quantum field theory - contents]]

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

\noindent\hyperlink{idea}{Idea}\dotfill \pageref*{idea} \linebreak
\noindent\hyperlink{bottomup_and_topdown_approaches}{Bottom-up and Top-down approaches}\dotfill \pageref*{bottomup_and_topdown_approaches} \linebreak
\noindent\hyperlink{properties}{Properties}\dotfill \pageref*{properties} \linebreak
\noindent\hyperlink{ChiralFermions}{Chiral fermions}\dotfill \pageref*{ChiralFermions} \linebreak
\noindent\hyperlink{GenerationsOfFermions}{Generations of fermions}\dotfill \pageref*{GenerationsOfFermions} \linebreak
\noindent\hyperlink{yukawa_couplings}{Yukawa couplings}\dotfill \pageref*{yukawa_couplings} \linebreak
\noindent\hyperlink{HiggsMechanism}{Higgs mechanism}\dotfill \pageref*{HiggsMechanism} \linebreak
\noindent\hyperlink{Orientifolding}{RR-Tadpole cancellation and Orientifolding}\dotfill \pageref*{Orientifolding} \linebreak
\noindent\hyperlink{IntersectionOfD6WithO8}{Intersections of D6s with D8/O8s}\dotfill \pageref*{IntersectionOfD6WithO8} \linebreak
\noindent\hyperlink{relation_to_mtheory_on_manifolds}{Relation to M-theory on $G_2$-manifolds}\dotfill \pageref*{relation_to_mtheory_on_manifolds} \linebreak
\noindent\hyperlink{Cosmology}{Cosmology and Holography}\dotfill \pageref*{Cosmology} \linebreak
\noindent\hyperlink{ComputerScanOfGepnerModelCompactifications}{Computer scan of Gepner-model compactifications}\dotfill \pageref*{ComputerScanOfGepnerModelCompactifications} \linebreak
\noindent\hyperlink{examples}{Examples}\dotfill \pageref*{examples} \linebreak
\noindent\hyperlink{intersecting_d6brane_models}{Intersecting D6-brane models}\dotfill \pageref*{intersecting_d6brane_models} \linebreak
\noindent\hyperlink{IntersectingD4BraneModels}{Intersecting D4-brane models}\dotfill \pageref*{IntersectingD4BraneModels} \linebreak
\noindent\hyperlink{references}{References}\dotfill \pageref*{references} \linebreak
\noindent\hyperlink{general}{General}\dotfill \pageref*{general} \linebreak
\noindent\hyperlink{the_landscape_of_models}{The landscape of models}\dotfill \pageref*{the_landscape_of_models} \linebreak
\noindent\hyperlink{ReferencesDetailedRealisticModels}{Detailed realistic models}\dotfill \pageref*{ReferencesDetailedRealisticModels} \linebreak
\noindent\hyperlink{ReferencesLiftToMTheory}{Lift to M-theory}\dotfill \pageref*{ReferencesLiftToMTheory} \linebreak
\noindent\hyperlink{ReferencesCosmology}{Cosmology}\dotfill \pageref*{ReferencesCosmology} \linebreak
\noindent\hyperlink{experimental_tests}{Experimental tests}\dotfill \pageref*{experimental_tests} \linebreak


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

In [[string phenomenology]] for [[type IIA string theory]], quasi-realistic [[model (physics)|models]] (i.e. close to the [[standard model of particle physics]], or an [[MSSM]]) may be obtained by [[KK-compactifications]] from the 10-[[dimensions]] down to 4d with configurations of [[D6-branes]] which fill all of 4d spacetime and [[brane intersection|intersect]] in a certain way in the 6-dimensional [[fiber]] space.



\begin{quote}%
graphics grabbed from \hyperlink{Uranga12a}{Uranga 12a, p. 12}


\end{quote}
The [[Chan-Paton gauge field]] on the [[D6-branes]] yields the [[gauge fields]] in 4d, and the precise [[brane intersection|intersection]] pattern determines the effective [[fundamental particle]] content in 4d.

See also at [[string phenomenology]] the section \emph{\href{string+phenomenology#ModelsInTypeIIWithIntersectingBranes}{Models in type II with intersecting branes}}.

\hypertarget{bottomup_and_topdown_approaches}{}\subsection*{{Bottom-up and Top-down approaches}}\label{bottomup_and_topdown_approaches}

One distinguishes [[bottom-up and top-down model building]] strategies:



\begin{quote}%
snippet grabbed from \hyperlink{AldazabalIbanezQuevedoUranga00}{Aldazabal-Ibáñez-Quevedo-Uranga 00}


\end{quote}
\hypertarget{properties}{}\subsection*{{Properties}}\label{properties}

\hypertarget{ChiralFermions}{}\subsubsection*{{Chiral fermions}}\label{ChiralFermions}

One of the most striking special properties of the [[standard model of particle physics]] is that its content of [[fermionic]] [[fundamental particles]] is ``[[chiral fermion|chiral]]'', in that the left and right [[Weyl spinor]]-components of the would-be [[Dirac spinor]]-representation of the [[quarks]], [[electrons]] and [[neutrinos]] couple \emph{differently} to the [[gauge fields]] (for review see e.g. \hyperlink{IbanezUranga12}{Ibanez-Uranga 12, section 1.1}).

The observation that such [[Weyl spinor|chiral fermions]] do indeed appear when [[D6-branes]] [[brane intersection|intersect]] at an angle on an $\mathbb{R}^{3,1}$ is due to (\hyperlink{BerkoozDouglasLeigh96}{Berkooz-Douglas-Leigh 96}), see also (\hyperlink{AFIRU00}{AFIRU 00, section 4}, \hyperlink{BCLS05}{BCLS 05, section 2.3}). For review with an eye towards [[RR-field tadpole cancellation]] on [[toroidal orbifold|toroidal]] [[orientifolds]] see also \hyperlink{ForsteHoneckerSchreyer01}{Forste-Honecker-Schreyer 01}, \hyperlink{Honecker01}{Honecker 01, Sec. 2}, \hyperlink{Honecker02}{Honecker 02}.



\begin{quote}%
graphics grabbed from \hyperlink{IbanezUranga12}{Ibáñez-Uranga 12}


\end{quote}
Vague review is in (\hyperlink{IbanezUranga12}{Ibáñez-Uranga 12, section 10.2.1}, \hyperlink{Uranga12a}{Uranga 12a, section 2.3}).

The lift of this situation to [[M-theory on G2-manifolds]] is discussed in (\hyperlink{BerglundBrandhuber02}{Berglund-Brandhuber 02}, \hyperlink{BourjailyEspahbodi08}{Bourjaily-Espahbodi 08}).

\hypertarget{GenerationsOfFermions}{}\subsubsection*{{Generations of fermions}}\label{GenerationsOfFermions}

While (presently) intersecting D-brane models don't explain why there are \emph{precisely} 3 [[generations of fundamental particles]] in the [[standard model of particle physics]], they do have the property that generically any such model does feature several [[generations of fundamental particles]].

The reason is that in these models there is one copy of a set of fundamental particles at each intersection point of two 3-manifolds (the internal part of the D6-branes) in a compact 6-dimensional space, and generically these intersection numbers are greater than one and hence induce a finite number of [[generations of fundamental particles|generations]] (\hyperlink{BCLS05}{BCLS 05, section 2.3}, \hyperlink{IbanezUranga12}{Ibanez-Uranga 12, p. 307}, \hyperlink{Uranga12a}{Uranga 12a, p. 12}):



\begin{quote}%
graphics grabbed from \hyperlink{Uranga12a}{Uranga 12a, p. 13}


\end{quote}
\hypertarget{yukawa_couplings}{}\subsubsection*{{Yukawa couplings}}\label{yukawa_couplings}

In [[intersecting D-brane models]] [[Yukawa couplings]] are encoded by [[worldsheet instantons]] of open strings stretching between the [[brane intersection|intersecting]] [[D-branes]] (see \hyperlink{Marchesano03}{Marchesano 03, Section 7.5}). Mathematically this is encoded by [[derived hom-spaces]] in a [[Fukaya category]] (see \hyperlink{Marchesano03}{Marchesano 03, Section 7.5}).

$\backslash$begin\{center\}  $\backslash$end\{center\}

\begin{quote}%
table grabbed from \hyperlink{Marchesano03}{Marchesano 03}


\end{quote}
Realistic [[Yukawa couplings]] and [[fermion]] [[masses]] in an [[MSSM]] [[Pati-Salam GUT model]] with 3 [[generations of fermions]] realized on [[intersecting D-brane model|intersecting]] [[D6-branes]] [[KK-compactification|KK-compactified]] on a [[toroidal orbifold]] $T^6\sslash (\mathbb{Z}_2 \times \mathbb{Z}_2)$ are claimed in in \hyperlink{Mayes19}{Mayes 19}, \hyperlink{GemillHowingtonMayes19}{Gemill-Howington-Mayes 19}, based on \hyperlink{ChenLiMayesNanopoulos07a}{Chen-Li-Mayes-Nanopoulos 07a}, \hyperlink{ChenLiMayesNanopoulos07b}{Chen-Li-Mayes-Nanopoulos 07b}.

$\backslash$linebreak

\hypertarget{HiggsMechanism}{}\subsubsection*{{Higgs mechanism}}\label{HiggsMechanism}

The [[Higgs mechanism]] naturally arises in [[intersecting D-brane models]]: The [[Higgs field]] appears here as the [[scalar field]] that witnesses in [[perturbative quantum field theory|perturbation theory]] the process of \emph{brane recombination} at the intersection locus of the D-branes (\hyperlink{CremadesIbanezMarchesano02}{Cremades-Ibanez-Marchesano 02, section 7}):



Further developments in \hyperlink{IbanezMarchesanoRabadan01}{Ibanez-Marchesano-Rabadan 01}, \hyperlink{HebeckerKnochelWeigand13}{Hebecker-Knochel-Weigand 13} and specifically via [[string field theory]] in \hyperlink{HINSS18}{HINSS 18}.

For review see \hyperlink{IbanezUranga12}{Ibanez-Uranga 12, fig 10.2}:



$\backslash$linebreak

\hypertarget{Orientifolding}{}\subsubsection*{{RR-Tadpole cancellation and Orientifolding}}\label{Orientifolding}

Consistent intersecting D-brane models have to be in [[type I string theory]], or generally in [[type II string theory]] with [[orientifold]] backgrounds, to achieve [[RR-field tadpole cancellation]].

This is a key consistency condition in intersecting D-brane model building (e.g. \hyperlink{BCLS05}{BCLS 05, section 2.4}, \hyperlink{IbanezUranga12}{Ibanez-Uranga 12, section 4.4})

[[!include RR-field tadpole cancellation on toroidal orientifolds -- table]]

\hypertarget{IntersectionOfD6WithO8}{}\subsubsection*{{Intersections of D6s with D8/O8s}}\label{IntersectionOfD6WithO8}

A [[black brane|black]] [[D6-brane]] may end on a [[black brane|black]] [[NS5-brane]], and in fact each [[black brane|brane]] [[NS5-brane]] at a non-trivial [[ADE singularity]] has to be the junction of two [[black brane|black]] [[D6-branes]]. For details see at \emph{\href{NS5-brane#D6BranesEndingOnNS5Branes}{D6-branes ending on NS5-branes}}.



\begin{quote}%
from \hyperlink{GKSTY02}{GKSTY 02}


\end{quote}
If in addition the [[black brane|black]] [[NS5-brane]] sits at an [[O8-plane]], hence at the [[orientifold]] [[fixed point]]-locus (see \hyperlink{Orientifolding}{above}), then in the ordinary $\mathbb{Z}/2$-[[quotient]] it appears as a ``[[half-brane]]'' with only one copy of [[D6-branes]] ending on it:



\begin{quote}%
from \hyperlink{GKSTY02}{GKSTY 02}


\end{quote}
(In \hyperlink{HananyZaffaroni99}{Hanany-Zaffaroni 99} this is interpreted in terms of the [[`t Hooft-Polyakov monopole]].)

The lift to [[M-theory]] of this situation is an [[M5-brane]] intersecting an [[M9-brane]]:



\begin{quote}%
from \hyperlink{GKSTY02}{GKSTY 02}


\end{quote}
Alternatively, the [[O8-plane]] may intersect the [[black brane|black]] [[D6-branes]] away from the [[black brane|black]] [[NS5-brane]]:



\begin{quote}%
from \hyperlink{HKLY15}{HKLY 15}


\end{quote}
In general, some of the NS5 sit away from the [[O8-plane]], while some sit on top of it:



\begin{quote}%
from \hyperlink{HananyZaffaroni98}{Hanany-Zaffaroni 98}


\end{quote}
\hypertarget{relation_to_mtheory_on_manifolds}{}\subsubsection*{{Relation to M-theory on $G_2$-manifolds}}\label{relation_to_mtheory_on_manifolds}

Lift to [[M-theory on G2-manifolds]] (e.g. [[G2-MSSM]]): see references \hyperlink{ReferencesLiftToMTheory}{below}

$\,$

\hypertarget{Cosmology}{}\subsubsection*{{Cosmology and Holography}}\label{Cosmology}

Since the [[near horizon geometry]] of [[BPS state|BPS]] [[black branes]] is conformal to the [[Cartesian product]] of [[anti de Sitter spaces]] with the unit $n$-sphere around the brane, the [[cosmology]] of intersecting D-brane models realizes the [[observable universe]] on the [[asymptotic boundary]] of an \emph{approximately} [[anti de Sitter spacetime]] (see for instance \hyperlink{Kaloper04}{Kaloper 04}, \hyperlink{FlachiMinamitsuji09}{Flachi-Minamitsuji 09}). The basic structure is hence that of \emph{[[Randall-Sundrum models]]}, but details differ, such as notably in \emph{warped throat} geometries, see \hyperlink{Uranga05}{Uranga 05, section 18}.

These warped throat models go back to \hyperlink{KlebanovStrassler00}{Klebanov-Strassler 00} which discusses aspects of [[confinement]] in [[Yang-Mills theory]] on conincident ordinary and \emph{[[fractional D-brane|fractional]]} [[D3-branes]] at the [[singularity]] of a warped [[conifold]]. See also \hyperlink{KlebanovWitten98}{Klebanov-Witten 98}.

\begin{quote}%
snippet grabbed from \hyperlink{Uranga05}{Uranga 05, section 18}

here: ``RS''=[[Randall-Sundrum model]]; ``KS''=\hyperlink{KlebanovStrassler00}{Klebanov-Strassler 00}


\end{quote}
In particular this means that [[AdS-CFT duality]] applies in \emph{some approximation} to intersecting D-brane models (e.g. \hyperlink{Soda10}{Soda 10}, \hyperlink{GHMO16}{GHMO 16}), thus allowing to compute, to some approximation, [[non-perturbative effects]] in the [[Yang-Mills theory]] on the intersecting branes in terms of [[gravity]] on the ambient warped throat $\sim$ [[anti de Sitter spacetime|AdS]] (\hyperlink{KlebanovStrassler00}{Klebanov-Strassler 00, section 6})

Such approximate versions of [[AdS-CFT]] for gauge theories realized on intersecting D-branes are used for instance to estimate [[non-perturbative effects]] in [[QCD]], such as the [[shear viscosity]] of the [[quark-gluon plasma]] (see the references \href{quark-gluon+plasma#ReferencesViaAdSCFT}{there}). See at \emph{[[AdS-QCD correspondence]]} for more on this.

$\,$

\hypertarget{ComputerScanOfGepnerModelCompactifications}{}\subsubsection*{{Computer scan of Gepner-model compactifications}}\label{ComputerScanOfGepnerModelCompactifications}

Discussion of [[string phenomenology]] of [[intersecting D-brane models]] [[KK-compactification|KK-compactified]] with non-geometric [[fibers]] such that the would-be string [[sigma-models]] with these [[target spaces]] are in fact [[Gepner models]] (in the sense of \emph{\href{https://www.physicsforums.com/insights/spectral-standard-model-string-compactifications/}{Spectral Standard Model and String Compactifications}}) is in (\hyperlink{DijkstraHuiszoonSchellekens04a}{Dijkstra-Huiszoon-Schellekens 04a}, \hyperlink{DijkstraHuiszoonSchellekens04a}{Dijkstra-Huiszoon-Schellekens 04b}):

\begin{quote}%
A plot of [[standard model of particle physics|standard model]]-like [[coupling constants]] in a computer scan of [[Gepner model]]-[[KK-compactification]] of [[intersecting D-brane models]] according to \hyperlink{DijkstraHuiszoonSchellekens04b}{Dijkstra-Huiszoon-Schellekens 04b}.

The blue dot indicates the couplings in $SU(5)$-[[GUT]] theory. The faint lines are NOT drawn by hand, but reflect increased density of Gepner models as seen by the computer scan.


\end{quote}
\hypertarget{examples}{}\subsection*{{Examples}}\label{examples}

\hypertarget{intersecting_d6brane_models}{}\subsubsection*{{Intersecting D6-brane models}}\label{intersecting_d6brane_models}

(\ldots{})

\begin{itemize}%
\item S. Ishihara, H. Kataoka, Hikaru Sato, \emph{$D=4$, $N=1$, Type IIA Orientifolds}, Phys. Rev. D60 (1999) 126005 (\href{https://arxiv.org/abs/hep-th/9908017}{arXiv:hep-th/9908017})

\end{itemize}
(\ldots{})

\hypertarget{IntersectingD4BraneModels}{}\subsubsection*{{Intersecting D4-brane models}}\label{IntersectingD4BraneModels}

Only [[D4-branes]]:

\begin{itemize}%
\item D. Bailin, G. V. Kraniotis, A. Love, \emph{Standard-like models from intersecting D4-branes}, Phys. Lett. B530 (2002) 202-209 (\href{https://arxiv.org/abs/hep-th/0108131}{arXiv:hep-th/0108131})


\item H. Kataoka, M. Shimojo, \emph{$SU(3) \times SU(2) \times U(1)$ Chiral Models from Intersecting D4-/D5-branes}, Progress of Theoretical Physics, Volume 107, Issue 6, June 2002, Pages 1291–1296 (\href{https://arxiv.org/abs/hep-th/0112247}{arXiv:hep-th/0112247}, \href{https://doi.org/10.1143/PTP.107.1291}{doi:10.1143/PTP.107.1291})


\item D. Bailin, \emph{Standard-like models from D-branes}, J Phys (2003) 60: 199 (\href{https://arxiv.org/abs/hep-th/0210227}{arXiv:hep-th/0210227})


\item D. Bailin, G. V. Kraniotis, A. Love, \emph{New Standard-like Models from Intersecting D4-Branes}, Phys. Lett. B547 (2002) 43-50 (\href{https://arxiv.org/abs/hep-th/0208103}{arXiv:hep-th/0208103})



\end{itemize}
[[D4-D8 brane bound states]]:

give the [[Witten-Sakai-Sugimoto model]] for [[holographic QCD]]

\begin{quote}%
graphics grabbed from \href{WSS-model#Erlich09}{Erlich 09, section 1.1}


\end{quote}
\begin{quote}%
graphics grabbed from \href{WSS-model#Rebhan14}{Rebhan 14}


\end{quote}
(\ldots{})

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

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

The [[bottom-up model building|bottom-up approach]] to intersecting D-brane model building was initiated in

\begin{itemize}%
\item G. Aldazabal, [[Luis Ibáñez]], F. Quevedo, [[Angel Uranga]], \emph{D-Branes at Singularities : A Bottom-Up Approach to the String Embedding of the Standard Model}, JHEP 0008:002 2000 (\href{http://xxx.lanl.gov/abs/hep-th/0005067}{arXiv:hep-th/0005067})

\end{itemize}
The observation that [[Weyl spinor|chiral fermions]] appear when [[D6-branes]] intersect at an angle is due to

\begin{itemize}%
\item [[Micha Berkooz]], [[Michael Douglas]], [[Robert Leigh]], \emph{Branes Intersecting at Angles}, Nucl.Phys.B480:265-278, 1996 (\href{https://arxiv.org/abs/hep-th/9606139}{arXiv:hep-th/9606139})

\end{itemize}
development for [[toroidal orbifold|toroidal]] [[orientifolds]] is due to

\begin{itemize}%
\item Stefan Forste, [[Gabriele Honecker]], Ralph Schreyer, \emph{Orientifolds with branes at angles}, JHEP 0106:004, 2001 (\href{https://arxiv.org/abs/hep-th/0105208}{arXiv:hep-th/0105208})


\item [[Gabriele Honecker]], \emph{Non-supersymmetric Orientifolds with D-branes at Angles}, Fortsch.Phys. 50 (2002) 896-902 (\href{https://arxiv.org/abs/hep-th/0112174}{arXiv:hep-th/0112174})


\item [[Gabriele Honecker]], \emph{Non-supersymmetric orientifolds and chiral fermions from intersecting D6- and D8-branes}, thesis 2002 ([[HoneckerIntersectingDBraneModels02.pdf:file]])



\end{itemize}
Review includes

\begin{itemize}%
\item G. Aldazabal, [[Luis Ibáñez]], F. Quevedo, \emph{On Realistic Brane Worlds from Type I Strings} (\href{https://arxiv.org/abs/hep-ph/0005033}{arXiv:hep-ph/0005033})


\item [[Fernando Marchesano]], \emph{Intersecting D-brane Models} (\href{https://arxiv.org/abs/hep-th/0307252}{arXiv:hep-th/0307252})


\item [[Ralph Blumenhagen]], [[Mirjam Cvetic]], Paul Langacker, [[Gary Shiu]], \emph{Towards Realistic Intersecting D-Brane Models}, Ann. Rev. Nucl. Part. Sci. 55:71-139, 2005 (\href{http://arxiv.org/abs/hep-th/0502005}{arXiv:hep-th/0502005})



\end{itemize}
A textbook account is

\begin{itemize}%
\item [[Luis Ibáñez]], [[Angel Uranga]], \emph{[[String Theory and Particle Physics -- An Introduction to String Phenomenology]]}, Cambridge 2012

\end{itemize}
Some chapters of which appear separately:

for [[D6-branes]]:

\begin{itemize}%
\item \hyperlink{AldazabalIbanezQuevedoUranga00}{Aldazabal-Ibanez-Quevedo-Uranga 00, section 10.2}


\item [[Angel Uranga]], \emph{Model building in IIA: Intersecting brane worlds}, 2012 (\href{http://scgp.stonybrook.edu/wp-content/uploads/2012/05/Uranga-Lecture-Notes-1.pdf}{pdf}, [[Uranga12.pdf:file]])



\end{itemize}
for [[D7-branes]]:

\begin{itemize}%
\item [[Angel Uranga]], \emph{Model building in type IIB string theory}, 2012 (\href{http://scgp.stonybrook.edu/wp-content/uploads/2012/05/Uranga-Lecture-Notes-2.pdf}{pdf})


\item Anshuman Maharana, [[Eran Palti]], \emph{Models of Particle Physics from Type IIB String Theory and F-theory: A Review} (\href{http://arxiv.org/abs/1212.0555}{arXiv:1212.0555})



\end{itemize}
Discussion of the [[Higgs mechanism]] in intersecting D-brane models:

\begin{itemize}%
\item [[Luis Ibáñez]], [[Fernando Marchesano]], R. Rabadan, section 7 of \emph{Getting just the Standard Model at Intersecting Branes}, JHEP 0111:002, 2001 (\href{https://arxiv.org/abs/hep-th/0105155}{arXiv:hep-th/0105155})


\item D. Cremades, [[Luis Ibáñez]], [[Fernando Marchesano]], \emph{Intersecting brane models of particle physics and the Higgs mechanism}, JHEP, 0207, 022 2002 (\href{https://arxiv.org/abs/hep-th/0203160}{arXiv:hep-th/0203160})


\item Arthur Hebecker, Alexander K. Knochel, [[Timo Weigand]], \emph{The Higgs mass from a String-Theoretic Perspective}, Nucl.Phys. B874 (2013) 1-35 (\href{https://arxiv.org/abs/1304.2767}{arXiv:1304.2767})


\item Manami Noumi Hashi, Hiroshi Isono, Toshifumi Noumi, Gary Shiu, Pablo Soler, \emph{Higgs Mechanism in Nonlocal Field Theories}, JHEP08 (2018) 064 (\href{https://arxiv.org/abs/1805.02676}{arXiv:1805.02676})



\end{itemize}
See also

\begin{itemize}%
\item G. Aldazabal, S. Franco, [[Luis Ibáñez]], R. Rabadan, A. M. Uranga, \emph{$D=4$ Chiral String Compactifications from Intersecting Branes}, J.Math.Phys.42:3103-3126, 2001 (\href{https://arxiv.org/abs/hep-th/0011073}{arXiv:hep-th/0011073})


\item [[Ralph Blumenhagen]], [[Volker Braun]], Boris Kors, [[Dieter Lüst]], \emph{The Standard Model on the Quintic}, Summary of Talks at SUSY02, 1st Intl. Conference on String Phenomenology in Oxford, Strings 2002 and 35th Ahrenshoop Symposium. (\href{http://arxiv.org/abs/hep-th/0210083}{arXiv:hep-th/0210083})


\item [[Dieter Lüst]], \emph{Intersecting Brane Worlds -- A Path to the Standard Model?}, Class. Quant. Grav.21 : S1399-1424, 2004 (\href{http://arxiv.org/abs/hep-th/0401156}{arXiv:hep-th/0401156})


\item Ching-Ming Chen, Tianjun Li, Dimitri V. Nanopoulos, \emph{Standard-Like Model Building on Type II Orientifolds}, Nucl.Phys.B732:224-242,2006 (\href{http://arxiv.org/abs/hep-th/0509059}{arXiv:hep-th/0509059})


\item [[Angel Uranga]], \emph{The standard model from D-branes in string theory}, talk at Padova, January 2008 (\href{http://active.pd.infn.it/g4/seminars/2008/files/uranga.pdf}{pdf})


\item Matthew J. Dolan, Sven Krippendorf, Fernando Quevedo, \emph{Towards a Systematic Construction of Realistic D-brane Models on a del Pezzo Singularity}, JHEP 1110 (2011) 024 (\href{http://arxiv.org/abs/1106.6039}{arXiv:1106.6039})


\item Yuta Hamada, Tatsuo Kobayashi, Shohei Uemura, \emph{Standard Model-like D-brane models and gauge couplings}, Nuclear Physics B Volume 897, August 2015, Pages 563-582 (\href{https://arxiv.org/abs/1409.2740}{arXiv:1409.2740})


\item Jill Ecker, [[Gabriele Honecker]], Wieland Staessens, \emph{D6-Brane Model Building on $\mathbb{Z}_2 \times \mathbb{Z}_6$: MSSM-like and Left-Right Symmetric Models}, Nuclear Physics B Volume 901, December 2015, Pages 139-215, (\href{https://arxiv.org/abs/1509.00048}{arXiv:1509.00048})



\end{itemize}
Intersection with [[O8-planes]]/[[D8-branes]] ([[M-theory on S1/G\_HW times H/G\_ADE]]) is discussed in

\begin{itemize}%
\item [[Amihay Hanany]], [[Alberto Zaffaroni]], \emph{Branes and Six Dimensional Supersymmetric Theories}, Nucl.Phys. B529 (1998) 180-206 (\href{https://arxiv.org/abs/hep-th/9712145}{arXiv:hep-th/9712145})


\item [[Amihay Hanany]], [[Alberto Zaffaroni]], \emph{Monopoles in String Theory}, JHEP 9912 (1999) 014 (\href{https://arxiv.org/abs/hep-th/9911113}{arXiv:hep-th/9911113})


\item E. Gorbatov, V.S. Kaplunovsky, J. Sonnenschein, [[Stefan Theisen]], S. Yankielowicz, \emph{On Heterotic Orbifolds, M Theory and Type I' Brane Engineering}, JHEP 0205:015, 2002 (\href{https://arxiv.org/abs/hep-th/0108135}{arXiv:hep-th/0108135})


\item Hirotaka Hayashi, Sung-Soo Kim, Kimyeong Lee, Futoshi Yagi, \emph{6d SCFTs, 5d Dualities and Tao Web Diagrams} (\href{https://arxiv.org/abs/1509.03300}{arXiv:1509.03300})



\end{itemize}
\hypertarget{the_landscape_of_models}{}\subsubsection*{{The landscape of models}}\label{the_landscape_of_models}

On the [[landscape of string theory vacua|landscape]] of intersecting D-brane models:

Computer scan of [[Gepner model]]-[[KK-compactifications]] of intersecting D-brane models:

\begin{itemize}%
\item T.P.T. Dijkstra, L. R. Huiszoon, [[Bert Schellekens]], \emph{Chiral Supersymmetric Standard Model Spectra from Orientifolds of Gepner Models}, Phys.Lett. B609 (2005) 408-417 (\href{https://arxiv.org/abs/hep-th/0403196}{arXiv:hep-th/0403196})


\item T.P.T. Dijkstra, L. R. Huiszoon, [[Bert Schellekens]], \emph{Supersymmetric Standard Model Spectra from RCFT orientifolds}, Nucl.Phys.B710:3-57,2005 (\href{https://arxiv.org/abs/hep-th/0411129}{arXiv:hep-th/0411129})



\end{itemize}
Computer scan of [[toroidal orbifold]]-[[KK compactifications]] is discussed in

\begin{itemize}%
\item [[Ralph Blumenhagen]], [[Florian Gmeiner]], [[Gabriele Honecker]], [[Dieter Lüst]], [[Timo Weigand]], \emph{The Statistics of Supersymmetric D-brane Models}, Nucl.Phys.B713:83-135, 2005 (\href{https://arxiv.org/abs/hep-th/0411173}{arXiv:hep-th/0411173})


\item [[Florian Gmeiner]], [[Ralph Blumenhagen]], [[Gabriele Honecker]], [[Dieter Lüst]], [[Timo Weigand]], \emph{One in a Billion: MSSM-like D-Brane Statistics}, JHEP 0601:004, 2006 (\href{https://arxiv.org/abs/hep-th/0510170}{arXiv:hep-th/0510170})



\end{itemize}
\hypertarget{ReferencesDetailedRealisticModels}{}\subsubsection*{{Detailed realistic models}}\label{ReferencesDetailedRealisticModels}

Realistic [[Yukawa couplings]] and [[fermion]] [[masses]] in an [[MSSM]] [[Pati-Salam GUT model]] with 3 [[generations of fermions]] realized on [[intersecting D-brane model|intersecting]] [[D6-branes]] [[KK-compactification|KK-compactified]] on a [[toroidal orbifold]] $T^6\sslash (\mathbb{Z}_2 \times \mathbb{Z}_2)$ are claimed in

\begin{itemize}%
\item Ching-Ming Chen, Tianjun Li, [[Van Eric Mayes]], [[Dimitri Nanopoulos]], \emph{A Realistic World from Intersecting D6-Branes}, Phys.Lett.B665:267-270, 2008 (\href{https://arxiv.org/abs/hep-th/0703280}{arXiv:hep-th/0703280}, \href{https://doi.org/10.1016/j.physletb.2008.06.024}{doi:10.1016/j.physletb.2008.06.024})


\item Ching-Ming Chen, Tianjun Li, [[Van Eric Mayes]], [[Dimitri Nanopoulos]], \emph{Realistic Yukawa Textures and SUSY Spectra from Intersecting Branes}, Phys.Rev.D77:125023, 2008 (\href{https://arxiv.org/abs/0711.0396}{arXiv:0711.0396})


\item [[Van Eric Mayes]], \emph{All Fermion Masses and Mixings in an Intersecting D-brane World} (\href{https://arxiv.org/abs/1902.00983}{arXiv:1902.00983})


\item Jordan Gemmill, Evan Howington, [[Van Eric Mayes]], \emph{One String to Rule Them All: Neutrino Masses and Mixing Angles} (\href{https://arxiv.org/abs/1907.07106}{arXiv:1907.07106})


\item Tianjun Li, Adeel Mansha, Rui Sun, \emph{Revisiting the Supersymmetric Pati-Salam Models from Intersecting D6-branes} (\href{https://arxiv.org/abs/1910.04530}{arXiv:1910.04530})



\end{itemize}
\hypertarget{ReferencesLiftToMTheory}{}\subsubsection*{{Lift to M-theory}}\label{ReferencesLiftToMTheory}

Lift of intersecting D-brane models to [[M-theory on G2-manifolds]] with [[ADE-singularities]] is discussed in the following articles

\begin{itemize}%
\item Per Berglund, Andreas Brandhuber, \emph{Matter from $G_2$-manifolds}, Nucl.Phys. B641 (2002) 351-375 (\href{https://arxiv.org/abs/hep-th/0205184}{arXiv:hep-th/0205184})


\item K. Behrndt, [[Gianguido Dall'Agata]], [[Dieter Lüst]], S. Mahapatra, \emph{Intersecting 6-branes from new 7-manifolds with G}2 holonomy\_, JHEP 0208:027,2002 (\href{https://arxiv.org/abs/hep-th/0207117}{arXiv:hep-th/0207117})


\item \hyperlink{BCLS05}{BCLS 05, section 2.9}


\item Jacob L. Bourjaily, Sam Espahbodi, \emph{Geometrically Engineerable Chiral Matter in M-Theory} (\href{https://arxiv.org/abs/0804.1132}{arXiv:0804.1132})



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

Discussion for [[cosmology]] of [[intersecting D-brane models]] (ambient $\sim$ [[anti de Sitter spacetimes]] with the $\sim$ conformal intersecting branes at the [[asymptotic boundary]]) includes the following (see also at \emph{[[Randall-Sundrum model]]}):

\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})


\item Luis Anchordoqui, Jose Edelstein, Carlos Nunez, Santiago Perez Bergliaffa, Martin Schvellinger, Marta Trobo, Fabio Zyserman, \emph{Brane Worlds, String Cosmology, and AdS/CFT}, Phys. Rev. D64:084027, 2001 (\href{https://arxiv.org/abs/hep-th/0106127}{arXiv:hep-th/0106127})


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


\item [[Angel Uranga]], section 18 of \emph{TASI lectures on String Compactification, Model Building, and Fluxes}, 2005 (\href{http://cds.cern.ch/record/933469/files/cer-002601054.pdf}{pdf}, \href{http:cds.cern.ch/record/933469}{cern:933469})


\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})


\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})


\item Gianluca Grignani, Troels Harmark, Andrea Marini, Marta Orselli, \emph{The Born-Infeld/Gravity Correspondence}, Phys. Rev. D 94, 066009 (2016) (\href{https://arxiv.org/abs/1602.01640}{arXiv:1602.01640})



\end{itemize}
Survey is in

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


\item Shunsuke Teraguchi, around slide 21 of: \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}
Discussion of 4d [[de Sitter spacetime]] [[cosmology]] models on brane worlds in $\sim$ [[anti de Sitter spacetime|AdS]] [[bulk]] spacetimes:

\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{experimental_tests}{}\subsubsection*{{Experimental tests}}\label{experimental_tests}

Discussion of observational/[[experiment|experimental]] test of brane world models:

by analysis of the [[event horizon]] of the [[black hole]] in the center of the [[galaxy]] [[Messier 87]]:

\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 intersecting D-brane models]]

[[!redirects intersecting D-brane model building]]

[[!redirects branes at angles]]

[[!redirects brane world model]] [[!redirects brane world models]]



\end{document}