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\begin{document}

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\section*{brane intersection}

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

\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{examples}{Examples}\dotfill \pageref*{examples} \linebreak
\noindent\hyperlink{12_m5brane}{1/2 M5-brane}\dotfill \pageref*{12_m5brane} \linebreak
\noindent\hyperlink{estring}{E-String}\dotfill \pageref*{estring} \linebreak
\noindent\hyperlink{string_network}{String network}\dotfill \pageref*{string_network} \linebreak
\noindent\hyperlink{membrane_triple_junction}{Membrane triple junction}\dotfill \pageref*{membrane_triple_junction} \linebreak
\noindent\hyperlink{d4branes_ending_on_d6branes}{D4-branes ending on D6-branes}\dotfill \pageref*{d4branes_ending_on_d6branes} \linebreak
\noindent\hyperlink{dpdp4_brane_intersections}{Dp-D(p+4) brane intersections}\dotfill \pageref*{dpdp4_brane_intersections} \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{BraneWebs}{Brane webs}\dotfill \pageref*{BraneWebs} \linebreak
\noindent\hyperlink{general_2}{General}\dotfill \pageref*{general_2} \linebreak
\noindent\hyperlink{ReferencesStringWebs}{String webs}\dotfill \pageref*{ReferencesStringWebs} \linebreak
\noindent\hyperlink{References5BraneWebs}{5-brane webs}\dotfill \pageref*{References5BraneWebs} \linebreak


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

[[intersection]] of [[branes]] in [[string theory]]

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

\hypertarget{12_m5brane}{}\subsubsection*{{1/2 M5-brane}}\label{12_m5brane}

[[M5-brane]] with [[KK-monopole]]:

\begin{displaymath}
(5\vert M5, KK)
  =
  \left\{
    \itexarray{
      x_0 & - & - & - & - & x_5 & x_6 & x_7 & x_8 & x_9 & -
      \\
      x_0 & A_1 & A_2 & A_3 & z & x_5 & x_6 & x_7 & x_8 & x_9 & x_{10}
    }
  \right.
\end{displaymath}
(\hyperlink{BREJS97}{BREJS 97 (14)})

For more see at \emph{\href{NS5-brane#NSHalfBranes}{Half NS5-branes}}

\hypertarget{estring}{}\subsubsection*{{E-String}}\label{estring}

See at \emph{[[E-string]]}

\hypertarget{string_network}{}\subsubsection*{{String network}}\label{string_network}

See at \emph{[[string network]]}.

\hypertarget{membrane_triple_junction}{}\subsubsection*{{Membrane triple junction}}\label{membrane_triple_junction}

see at \emph{[[membrane triple junction]]}.

\hypertarget{d4branes_ending_on_d6branes}{}\subsubsection*{{D4-branes ending on D6-branes}}\label{d4branes_ending_on_d6branes}

[[D4-branes]] ending on [[D6-branes]] from [[M5-branes]] in [[MK6-branes]]:

\hyperlink{Hashimotop98}{Hashimoto 98}, see also \hyperlink{Smith02}{Smith 02 (245)}

\hypertarget{dpdp4_brane_intersections}{}\subsubsection*{{Dp-D(p+4) brane intersections}}\label{dpdp4_brane_intersections}

[[!include Dp-D(p+4)-brane bound states -- contents]]

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

\begin{itemize}%
\item [[intersecting D-brane model]]


\item [[D1-D5 brane bound state]]



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

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

\begin{itemize}%
\item Douglas J. Smith, \emph{Intersecting brane solutions in string and M-theory}, Class.Quant.Grav.20:R233, 2003 (\href{https://arxiv.org/abs/hep-th/0210157}{arXiv:hep-th/0210157})


\item Akikazu Hashimoto, \emph{Supergravity Solutions for Localized Intersections of Branes}, JHEP 9901 (1999) 018 (\href{https://arxiv.org/abs/hep-th/9812159}{arXiv:hep-th/9812159})



\end{itemize}
For [[M-branes]]:

\begin{itemize}%
\item [[Eric Bergshoeff]], M. Roo, E. Eyras, [[Bert Janssen]], J. P. Schaar, \emph{Intersections involving waves and monopoles in eleven dimensions}, Class. Quantum Grav. 14 2757 (\href{https://arxiv.org/abs/hep-th/9704120}{arXiv:hep-th/9704120}, \href{http://iopscience.iop.org/0264-9381/14/10/005/}{publisher})


\item [[Eric Bergshoeff]], [[Joaquim Gomis]], [[Paul Townsend]], \emph{M-brane intersections from worldvolume superalgebras}, Phys.Lett. B421 (1998) 109-118 (\href{http://arxiv.org/abs/hep-th/9711043}{arXiv:hep-th/9711043})


\item [[Paul Townsend]], section 4 of \emph{M-theory from its superalgebra} (\href{http://arxiv.org/abs/hep-th/9712004}{arXiv:hep-th/9712004})


\item Sergey A. Cherkis, \emph{Supergravity Solution for M5-brane Intersection} (\href{https://arxiv.org/abs/hep-th/9906203}{arXiv:hep-th/9906203})



\end{itemize}
\hypertarget{BraneWebs}{}\subsubsection*{{Brane webs}}\label{BraneWebs}

Intersections of branes of equal dimension may form regular patterns known as \emph{brane webs}. This applies notably in [[type IIB string theory]] where [[(p,q)-strings]] may form ``[[string webs]]'' (references \hyperlink{ReferencesStringWebs}{below}) and [[(p,q)5-branes]] may form ``[[5-brane webs]]'' (references \hyperlink{References5BraneWebs}{further below})

\hypertarget{general_2}{}\paragraph*{{General}}\label{general_2}

\begin{itemize}%
\item Oleg Lunin, \emph{Brane webs and 1/4-BPS geometries}, JHEP09 (2008) (\href{https://arxiv.org/abs/0802.0735}{arXiv:0802.0735})

\end{itemize}
\hypertarget{ReferencesStringWebs}{}\paragraph*{{String webs}}\label{ReferencesStringWebs}

\begin{itemize}%
\item [[Ashoke Sen]], \emph{String Network}, JHEP 9803:005, 1998 (\href{https://arxiv.org/abs/hep-th/9711130}{arXiv:hep-th/9711130})


\item Soo-Jong Rey, Jung-Tay Yee, \emph{BPS Dynamics of Triple $(p,q)$ String Junction}, Nucl.Phys. B526 (1998) 229-240 (\href{https://arxiv.org/abs/hep-th/9711202}{arXiv:hep-th/9711202})


\item [[Keshav Dasgupta]], [[Sunil Mukhi]], \emph{BPS Nature of 3-String Junctions}, Phys.Lett. B423 (1998) 261-264 (\href{https://arxiv.org/abs/hep-th/9711094}{arXiv:hep-th/9711094})



\end{itemize}
Via [[tropical geometry]]:

\begin{itemize}%
\item Koushik Ray, \emph{String networks as tropical curves}, JHEP 0809:098, 2008 (\href{https://arxiv.org/abs/0804.1870}{arXiv:0804.1870})

\end{itemize}
The lift to [[11d supergravity]]/[[M-theory]] via [[membrane triple junctions]] is discussed in

\begin{itemize}%
\item Morten Krogh, Sangmin Lee, \emph{String Network from M-theory}, Nucl. Phys. B516:241-254, 1998 (\href{https://arxiv.org/abs/hep-th/9712050}{arXiv:hep-th/9712050})


\item P. Ramadevi, \emph{Supergravity Solution for Three-String Junction in M-Theory}, JHEP 0006 (2000) 005 (\href{https://arxiv.org/abs/hep-th/9906247}{arXiv:hep-th/9906247})



\end{itemize}
\hypertarget{References5BraneWebs}{}\paragraph*{{5-brane webs}}\label{References5BraneWebs}

\begin{itemize}%
\item [[Ofer Aharony]], [[Amihay Hanany]], section 3 of \emph{Branes, Superpotentials and Superconformal Fixed Points}, Nucl.Phys.B504:239-271, 1997 (\href{https://arxiv.org/abs/hep-th/9704170}{arXiv:hep-th/9704170})


\item [[Barak Kol]], \emph{5d Field Theories and M Theory}, JHEP 9911 (1999) 026 (\href{https://arxiv.org/abs/hep-th/9705031}{arXiv:hep-th/9705031})


\item [[Ofer Aharony]], [[Amihay Hanany]], [[Barak Kol]], \emph{Webs of $(p,q)$ 5-branes, Five Dimensional Field Theories and Grid Diagrams}, JHEP 9801:002,1998 (\href{http://arxiv.org/abs/hep-th/9710116}{arXiv:hep-th/9710116})


\item Francesco Benini, Sergio Benvenuti, Yuji Tachikawa, \emph{Webs of five-branes and $N=2$ superconformal field theories}, JHEP 0909:052,2009 (\href{https://arxiv.org/abs/0906.0359}{arXiv:0906.0359})


\item Sung-Soo Kim, Masato Taki, Futoshi Yagi, \emph{Tao Probing the End of the World}, Prog. Theor. Exp. Phys. 2015, 083B02 (\href{https://arxiv.org/abs/1504.03672}{arXiv:1504.03672})


\item Brice Bastian, Stefan Hohenegger, \emph{Five-Brane Webs and Highest Weight Representations} (\href{https://arxiv.org/abs/1706.08750}{arXiv:1706.08750})


\item Justin Kaidi, \emph{$(p,q)$-strings probing five-brane webs}, J. High Energ. Phys. (2017) 2017: 87 (\href{https://arxiv.org/abs/1708.03404}{arXiv:1708.03404})


\item Michael Gutperle, Andrea Trivella, Christoph F. Uhlemann, \emph{Type IIB 7-branes in warped $AdS_6$: partition functions, brane webs and probe limit}, JHEP04(2018)135 (\href{https://arxiv.org/abs/1802.07274}{arXiv:1802.07274})


\item Hirotaka Hayashi, Sung-Soo Kim, Kimyeong Lee, Futoshi Yagi, \emph{Dualities and 5-brane webs for 5d rank 2 SCFTs} (\href{https://arxiv.org/abs/1806.10569}{arXiv:1806.10569})



\end{itemize}
[[!redirects brane intersections]]

[[!redirects intersecting brane]] [[!redirects intersecting branes]]

[[!redirects brane web]] [[!redirects brane webs]]

[[!redirects 5-brane web]] [[!redirects 5-brane webs]]



\end{document}