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\begin{document}

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\section*{M5-MO9 brane bound state}

\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{in_string_theory}{In string theory}\dotfill \pageref*{in_string_theory} \linebreak
\noindent\hyperlink{AsYangMillsInstantons}{As Yang-Mills instantons in heterotic string theory}\dotfill \pageref*{AsYangMillsInstantons} \linebreak
\noindent\hyperlink{as_half_ns5branes_in_type_i}{As half NS5-branes in type I'}\dotfill \pageref*{as_half_ns5branes_in_type_i} \linebreak
\noindent\hyperlink{related_concepts}{Related concepts}\dotfill \pageref*{related_concepts} \linebreak
\noindent\hyperlink{references}{References}\dotfill \pageref*{references} \linebreak
\noindent\hyperlink{as_heterotic_yangmills_instantons}{As heterotic Yang-Mills instantons}\dotfill \pageref*{as_heterotic_yangmills_instantons} \linebreak
\noindent\hyperlink{as_half_m5branes}{As half M5-branes}\dotfill \pageref*{as_half_m5branes} \linebreak


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

The [[brane intersection]] of [[M5-branes]] with [[MO9-planes]] -- the ``half M5-brane''.

Equivalently:

\begin{itemize}%
\item under [[duality between M-theory and heterotic string theory]]: [[black brane|black]] [[NS5-brane]] [[solitons]] in [[heterotic string theory]].


\item under [[duality between M-theory and type IIA string theory]]:

[[D4-D8-brane bound states]] or \href{NS5-brane#NSHalfBranes}{half NS5-brane} in [[type I' string theory]]



\end{itemize}
\begin{quote}%
graphics grabbed from \hyperlink{HSS18}{HSS18, Example 2.2.7}


\end{quote}


\begin{quote}%
graphics grabbed from \hyperlink{SatiSchreiber19}{SS 19, Section 4}


\end{quote}
\hypertarget{in_string_theory}{}\subsection*{{In string theory}}\label{in_string_theory}

\hypertarget{AsYangMillsInstantons}{}\subsubsection*{{As Yang-Mills instantons in heterotic string theory}}\label{AsYangMillsInstantons}

In ([[dual heterotic string theory|dual]]) [[heterotic string theory]] [[wrapped brane|wrapped]] [[NS5-branes]] are equivalently [[Yang-Mills instantons]] in the transversal [[Yang-Mills theory]] (\hyperlink{Strominger90}{Strominger 90}, \hyperlink{Witten96}{Witten 96, p. 10}) -- as is generally the case for [[Dp-D(p+4)-brane bound states]] (see \href{DpDpPlus4BraneBoundState#AsYangMillsInstantons}{there}).

\hypertarget{as_half_ns5branes_in_type_i}{}\subsubsection*{{As half NS5-branes in type I'}}\label{as_half_ns5branes_in_type_i}

(For more see at \href{NS5-brane#NSHalfBranes}{half NS5-brane}.)

If a [[black brane|black]] [[NS5-brane]] sits at an [[O8-plane]], hence at the [[orientifold]] [[fixed point]]-locus, 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 \href{NS5-brane##GKSTY02}{GKSTY 02}


\end{quote}
(In \href{NS5-brane##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]] [[brane intersection|intersecting]] an [[M9-brane]] (see at \emph{[[MO5-plane]]} and at \emph{[[heterotic M-theory on ADE-orbifolds]]}):



\begin{quote}%
from \href{NS5-brane##GKSTY02}{GKSTY 02}


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



\begin{quote}%
from \href{NS5-brane##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 \href{NS5-brane##HananyZaffaroni98}{Hanany-Zaffaroni 98}


\end{quote}


\begin{quote}%
graphics grabbed from \href{NS5-brane##ApruzziFazzi17}{Apruzzi-Fazzi 17, p. 18}


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

\begin{itemize}%
\item [[heterotic M-theory on ADE-orbifolds]]


\item [[M2-M5 brane bound state]]


\item \href{NS5-brane#NS5D4D2BoundStates}{NS5-D4-D2 bound states}



\end{itemize}
[[!include Dp-D(p+4)-brane bound states -- contents]]

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

\hypertarget{as_heterotic_yangmills_instantons}{}\subsubsection*{{As heterotic Yang-Mills instantons}}\label{as_heterotic_yangmills_instantons}

Discussion as [[Yang-Mills instantons]] (``small instantons''):

\begin{itemize}%
\item [[Andrew Strominger]], \emph{Heterotic solitons}, Nucl. Phys. B343 (1990) 167-184 () Erratum: Nucl. Phys. B353 (1991) 565-565 () (\href{http://inspirehep.net/record/27900}{spire:27900})


\item [[Edward Witten]], \emph{Small Instantons in String Theory}, Nucl.Phys.B460:541-559, 1996 ()



\end{itemize}
\hypertarget{as_half_m5branes}{}\subsubsection*{{As half M5-branes}}\label{as_half_m5branes}

\begin{itemize}%
\item [[John Huerta]], [[Hisham Sati]], [[Urs Schreiber]], Example 2.2.7 of: \emph{[[schreiber:Equivariant homotopy and super M-branes|Real ADE-equivariant (co)homotopy and Super M-branes]]}, CMP (2019) (\href{https://arxiv.org/abs/1805.05987}{arXiv:1805.05987}, \href{http://link.springer.com/article/10.1007/s00220-019-03442-3}{doi:10.1007/s00220-019-03442-3})


\item [[Domenico Fiorenza]], [[Hisham Sati]], [[Urs Schreiber]], Section 4 of: \emph{[[schreiber:Super-exceptional embedding construction of the M5-brane|Super-exceptional geometry: origin of heterotic M-theory and super-exceptional embedding construction of M5]]} (\href{https://arxiv.org/abs/1908.00042}{arXiv:1908.00042})


\item [[nLab:Hisham Sati]], [[nLab:Urs Schreiber]], Section 4.1 of: \emph{[[schreiber:Equivariant Cohomotopy implies orientifold tadpole cancellation]]} (\href{https://arxiv.org/abs/1909.12277}{arXiv:1909.12277})



\end{itemize}
[[!redirects M5-MO9 brane bound states]]

[[!redirects half M5-brane]] [[!redirects half M5-branes]]



\end{document}