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\section*{D4-D8 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{properties}{Properties}\dotfill \pageref*{properties} \linebreak
\noindent\hyperlink{as_a_black_brane}{As a black brane}\dotfill \pageref*{as_a_black_brane} \linebreak
\noindent\hyperlink{AsGeometricEngineeringOfQCD}{As geometric engineering of QCD}\dotfill \pageref*{AsGeometricEngineeringOfQCD} \linebreak
\noindent\hyperlink{as_instantons_on_the_d8brane}{As instantons on the D8-brane}\dotfill \pageref*{as_instantons_on_the_d8brane} \linebreak
\noindent\hyperlink{related_entries}{Related entries}\dotfill \pageref*{related_entries} \linebreak
\noindent\hyperlink{references}{References}\dotfill \pageref*{references} \linebreak
\noindent\hyperlink{black_brane_solutions}{Black brane solutions}\dotfill \pageref*{black_brane_solutions} \linebreak
\noindent\hyperlink{as_geometric_engineering_of_qcd_2}{As geometric engineering of QCD}\dotfill \pageref*{as_geometric_engineering_of_qcd_2} \linebreak
\noindent\hyperlink{general_brane_bound_states}{General $D p$-$D(p+4)$-brane bound states}\dotfill \pageref*{general_brane_bound_states} \linebreak


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

[[bound states]] of [[D4-branes]] with [[D8-branes]]. A special case of the general phenomenon of [[Dp-D(p+4)-brane bound states]].

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

\hypertarget{as_a_black_brane}{}\subsubsection*{{As a black brane}}\label{as_a_black_brane}

As a [[black brane]] [[supergravity]] solution: \hyperlink{BrandhuberOz99}{Brandhuber-Oz 99}, \hyperlink{Nastase03}{Nastase 03, Sec. 2 and 3}, \hyperlink{BSU09}{BSU 09}, \hyperlink{VanPol15}{Van Pol 15, Sec 5}, \hyperlink{DibitettoPetri18}{Dibitetto-Petri 18}

\hypertarget{AsGeometricEngineeringOfQCD}{}\subsubsection*{{As geometric engineering of QCD}}\label{AsGeometricEngineeringOfQCD}

The D4-D8 system is the [[intersecting D-brane model]] underlying the [[Witten-Sakai-Sugimoto model]] for [[holographic QCD]]

\begin{quote}%
graphics grabbed from \hyperlink{Erlich09}{Erlich 09, section 1.1}


\end{quote}
\begin{quote}%
graphics grabbed from \hyperlink{Rebhan14}{Rebhan 14}


\end{quote}
\hypertarget{as_instantons_on_the_d8brane}{}\subsubsection*{{As instantons on the D8-brane}}\label{as_instantons_on_the_d8brane}

Generally, due to the [[higher WZW term]] $\propto \int_{D_{p+4}} C_{p+1} \wedge \langle F \wedge F \rangle$ in the [[Green-Schwarz sigma model]] for [[D-brane|D(p+4)-branes]], [[Yang-Mills instantons]] in the [[Chan-Paton gauge field]] on $D (p+4)$-branes are equivalently [[Dp-D(p+4)-brane bound states]] (see e.g. \hyperlink{Polchinski96}{Polchinski 96, 5.4}, \hyperlink{Tong05}{Tong 05, 1.4}).

In terms of [[holographic QCD]] as \hyperlink{AsGeometricEngineeringOfQCD}{above} these instantons correspond to [[baryon]]-[[bound states]] (\hyperlink{SakaiSugimoto04}{Sakai-Sugimoto 04, 5.7}).

\begin{quote}%
graphics grabbed from \href{AdS/QCD#Sugimoto16}{Sugimoto 16}


\end{quote}
\hypertarget{related_entries}{}\subsection*{{Related entries}}\label{related_entries}

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


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



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

\begin{itemize}%
\item [[bound state]]


\item [[brane intersection]]


\item [[wrapped brane]]



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

\hypertarget{black_brane_solutions}{}\subsubsection*{{Black brane solutions}}\label{black_brane_solutions}

As [[black brane]] [[supergravity]]-solutions:

\begin{itemize}%
\item [[Andreas Brandhuber]], [[Yaron Oz]], \emph{The D4-D8 Brane System and Five Dimensional Fixed Points}, Phys.Lett. B460:307-312, 1999 (\href{https://arxiv.org/abs/hep-th/9905148}{arXiv:hep-th/9905148})


\item [[Horatiu Nastase]], Sections 2, 3 of: \emph{On Dp-Dp+4 systems, QCD dual and phenomenology} (\href{https://arxiv.org/abs/hep-th/0305069}{arXiv:hep-th/0305069})


\item Pierre Binetruy, Misao Sasaki, Kunihito Uzawam, \emph{Dynamical D4-D8 and D3-D7 branes in supergravity}, Phys. Rev. D80:026001, 2009 (\href{https://arxiv.org/abs/0712.3615}{arXiv:0712.3615})


\item [[Oren Bergman]], Diego Rodriguez-Gomez, Section 2.3 of: \emph{5d quivers and their $AdS_6$ duals}, J. High Energ. Phys. (2012) 2012: 171 (\href{https://arxiv.org/abs/1206.3503}{arXiv:1206.3503})


\item Bert Van Pol, Section 5 of: \emph{Aspects of D-branes in supergravity}, thesis 2015 (\href{http://inspirehep.net/record/1404388/files/bertvanpol-phdthesis.pdf}{pdf}, [[VanPolThesis15.pdf:file]])


\item Giuseppe Dibitetto, Nicolò Petri, \emph{Surface defects in the D4-D8 brane system}, J. High Energ. Phys. (2019) 2019: 193 (\href{https://arxiv.org/abs/1807.07768}{arXiv:1807.07768})



\end{itemize}
\hypertarget{as_geometric_engineering_of_qcd_2}{}\subsubsection*{{As geometric engineering of QCD}}\label{as_geometric_engineering_of_qcd_2}

With application to [[geometric engineering of QFTs|geometric engineering]] of [[QCD]] (``[[holographic QCD]]'', such as the [[Witten-Sakai-Sugimoto model]]):

\begin{itemize}%
\item [[David Morrison]], [[Nathan Seiberg]], \emph{Extremal Transitions and Five-Dimensional Supersymmetric Field Theories}, Nucl. Phys.B483:229-247, 1997 (\href{https://arxiv.org/abs/hep-th/9609070}{arXiv:hep-th/9609070})


\item \hyperlink{Nastase03}{Nastase 03, Sec. 5}


\item Hee-Cheol Kim, Sung-Soo Kim, Kimyeong Lee, \emph{5-dim Superconformal Index with Enhanced En Global Symmetry}, JHEP 1210 (2012) 142 (\href{https://arxiv.org/abs/1206.6781}{arXiv:1206.6781})


\item Chiung Hwang, Joonho Kim, Seok Kim, Jaemo Park, \emph{General instanton counting and 5d SCFT} (\href{https://arxiv.org/abs/1406.6793}{arxiv:1406.6793})



\end{itemize}
Review:

\begin{itemize}%
\item Yolanda Lozano, Section 2 of: \emph{Hints on 5d Fixed Point Theories from Non-Abelian T-duality}, IFT 2014 (\href{https://www.unioviedo.es/hepth/people/Yolanda/talks/IFT2014.pdf}{slides pdf}, [[Lozano5d.pdf:file]])

\end{itemize}
As a model for [[baryons]]:

\begin{itemize}%
\item [[Tadakatsu Sakai]], [[Shigeki Sugimoto]], \emph{Low energy hadron physics in holographic QCD}, Prog. Theor. Phys.113:843-882, 2005 (\href{https://arxiv.org/abs/hep-th/0412141}{arXiv:hep-th/0412141})

\end{itemize}
Among review of the [[Witten-Sakai-Sugimoto model]]:

\begin{itemize}%
\item Joshua Erlich, \emph{How Well Does AdS/QCD Describe QCD?}, Int. J. Mod. Phys.A25:411-421,2010 (\href{https://arxiv.org/abs/0908.0312}{arXiv:0908.0312})


\item Anton Rebhan, \emph{The Witten-Sakai-Sugimoto model: A brief review and some recent results}, 3rd International Conference on New Frontiers in Physics, Kolymbari, Crete, 2014 (\href{https://arxiv.org/abs/1410.8858}{arXiv:1410.8858})



\end{itemize}
\hypertarget{general_brane_bound_states}{}\subsubsection*{{General $D p$-$D(p+4)$-brane bound states}}\label{general_brane_bound_states}

The argument that [[Yang-Mills instantons]] in the [[Chan-Paton gauge field]] on a [[D-brane|D(p+4)-brane]] are equivalent to [[Dp-D(p+4) brane bound states]] goes back to

\begin{itemize}%
\item [[Edward Witten]], \emph{Small Instantons in String Theory}, Nucl. Phys. B460:541-559, 1996 (\href{https://arxiv.org/abs/hep-th/9511030}{arXiv:hep-th/9511030})


\item [[Michael Douglas]], \emph{Gauge Fields and D-branes}, J. Geom. Phys. 28 (1998) 255-262 (\href{https://arxiv.org/abs/hep-th/9604198}{arXiv:hep-th/9604198})



\end{itemize}
Review is in:

\begin{itemize}%
\item [[Joseph Polchinski]], Section 5.4 of: \emph{TASI Lectures on D-Branes} (\href{https://arxiv.org/abs/hep-th/9611050}{arXiv:hep-th/9611050})


\item [[David Tong]], Section 1.4 of \emph{TASI Lectures on Solitons} (\href{https://arxiv.org/abs/hep-th/0509216}{hep-th/0509216})



\end{itemize}
Discussion specifically of [[D0-D4-brane bound states]]:

\begin{itemize}%
\item [[Cumrun Vafa]], \emph{Instantons on D-branes}, Nucl. Phys. B463 (1996) 435-442 (\href{https://arxiv.org/abs/hep-th/9512078}{arXiv:hep-th/9512078})

\end{itemize}
with emphasis to the resulting [[configuration spaces of points]], as in

\begin{itemize}%
\item [[Cumrun Vafa]], [[Edward Witten]], Section 4.1 of: \emph{A Strong Coupling Test of S-Duality}, Nucl. Phys. B431:3-77, 1994 (\href{https://arxiv.org/abs/hep-th/9408074}{arXiv:hep-th/9408074})

\end{itemize}
Discussion specifically of [[D1-D5-brane bound states]]

\begin{itemize}%
\item [[Neil Lambert]], \emph{D-brane Bound States and the Generalised ADHM Construction}, Nucl. Phys. B519 (1998) 214-224 (\href{https://arxiv.org/abs/hep-th/9707156}{arXiv:hep-th/9707156})

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

[[!redirects D4-D8-brane bound state]] [[!redirects D4-D8-brane bound states]]



\end{document}