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\newtheorem{prop}{Proposition} \newtheorem{cor}{Corollary} \newtheorem*{utheorem}{Theorem} \newtheorem*{ulemma}{Lemma} \newtheorem*{uprop}{Proposition} \newtheorem*{ucor}{Corollary} \theoremstyle{definition} \newtheorem{defn}{Definition} \newtheorem{example}{Example} \newtheorem*{udefn}{Definition} \newtheorem*{uexample}{Example} \theoremstyle{remark} \newtheorem{remark}{Remark} \newtheorem{note}{Note} \newtheorem*{uremark}{Remark} \newtheorem*{unote}{Note} %------------------------------------------------------------------- \begin{document} %------------------------------------------------------------------- \section*{orientifold plane} \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{TDualityWithTypeIStringTheory}{T-Duality with type I string theory}\dotfill \pageref*{TDualityWithTypeIStringTheory} \linebreak \noindent\hyperlink{OPlaneCharge}{O-Plane charge}\dotfill \pageref*{OPlaneCharge} \linebreak \noindent\hyperlink{OPlaneChargeForFlatOrientifolds}{For flat orientifolds}\dotfill \pageref*{OPlaneChargeForFlatOrientifolds} \linebreak \noindent\hyperlink{WithDiscreteTorsion}{In the presence of discrete torsion}\dotfill \pageref*{WithDiscreteTorsion} \linebreak \noindent\hyperlink{in_differential_equivariant_krtheory}{In differential equivariant KR-theory}\dotfill \pageref*{in_differential_equivariant_krtheory} \linebreak \noindent\hyperlink{DualityWithMTheory}{Duality with M-Theory}\dotfill \pageref*{DualityWithMTheory} \linebreak \noindent\hyperlink{fractional_branes_at_oplanes}{Fractional branes at O-planes}\dotfill \pageref*{fractional_branes_at_oplanes} \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{with_discrete_torsion}{With discrete torsion}\dotfill \pageref*{with_discrete_torsion} \linebreak \noindent\hyperlink{in_terms_of_kotheory}{In terms of KO-theory}\dotfill \pageref*{in_terms_of_kotheory} \linebreak \noindent\hyperlink{examples__models}{Examples / Models}\dotfill \pageref*{examples__models} \linebreak \noindent\hyperlink{lift_to_mtheory}{Lift to M-theory}\dotfill \pageref*{lift_to_mtheory} \linebreak \hypertarget{idea}{}\subsection*{{Idea}}\label{idea} In [[type II string theory]] on [[orientifolds]] (\hyperlink{DaiLinPolchinski89}{Dai-Lin-Polchinski 89}), one says \emph{O-plane} for the [[fixed point]] locus of the $\mathbb{Z}_2$-[[involution]] (see at \emph{[[real space]]}). O-planes carry [[D-brane charges]] in [[KR-theory]] (\hyperlink{Witten98}{Witten 98}), see (\hyperlink{DMR13}{DMR 13}) for a mathematical account. They serve [[RR-field tadpole cancellation]] and as such play a key role in the construction of [[intersecting D-brane models]] for [[string phenomenology]]. \hypertarget{properties}{}\subsection*{{Properties}}\label{properties} \hypertarget{TDualityWithTypeIStringTheory}{}\subsubsection*{{T-Duality with type I string theory}}\label{TDualityWithTypeIStringTheory} Under [[T-duality]], [[type I string theory]] is [[duality in string theory|dual]] to [[type II string theory]] with orientifold planes (reviewed e.g. in \hyperlink{IbanezUranga12}{Ibanez-Uranga 12, section 5.3.2 - 5.3.4}): \hypertarget{OPlaneCharge}{}\subsubsection*{{O-Plane charge}}\label{OPlaneCharge} O-planes carry effective negative [[RR-charge]] which may (must) cancel against the actual [[RR-charge|RR-]] [[D-brane charge]] via [[RR-field tadpole cancellation]]. \hypertarget{OPlaneChargeForFlatOrientifolds}{}\paragraph*{{For flat orientifolds}}\label{OPlaneChargeForFlatOrientifolds} The charge of the [[spacetime]]-filling $O9$-plane of plain [[type I string theory]] ([[type II string theory]] on the [[orientifold]] $\mathbb{R}^{9,1}\sslash \mathbb{Z}_2$ with [[trivial action|trival]] spacetime $\mathbb{Z}_2$-[[action]]) is found by [[worldsheet]]-computation to be $-32$ in [[physical unit|units]] of [[D9]]-[[D-brane charge|brane charge]]: \begin{equation} q_{O9^-} \;=\; -32 \, q_{D9} \label{O9PlaneCharge}\end{equation} (e.g. \hyperlink{BlumenhagenLustTheisen13}{Blumenhagen-Lüst-Theisen 13 (9.83)}). \begin{remark} \label{ContingOfDBranesOnOrientifolds}\hypertarget{ContingOfDBranesOnOrientifolds}{} \textbf{counting of D-branes on orientifolds} Beware that there is some convention involved in assigning an absolute value of unit D-brane charge $q_{D9}$. A common choice in the literature is to mean by ``one D-brane'' one of the two pre-images on the [[covering space]], in which case its obsolute charge is to be \begin{equation} q_{Dp} \;=\; 1/2 \label{DBraneChargeOnOrbifold}\end{equation} (e.g. \hyperlink{BDHKMMS01}{BDHKMMS 01, p. 46-47}). From \hyperlink{BlumenhagenLustTheisen13}{BLT 13, p. 318}: \end{remark} This means that [[RR-field tadpole cancellation]] here requires the presence of 32 [[D-branes]] (or rather, by Remark \ref{ContingOfDBranesOnOrientifolds}: 16 and their $\mathbb{Z}_2$-mirror images), hence a space-filling [[D9-brane]] with [[Chan-Paton bundle]] of [[rank of a vector bundle|rank]] $32$, corresponding to a [[gauge group]] [[SO(32)]]. For more on this see at \emph{[[type I string theory]] -- \href{type+I+string+theory#TadpoleCancellationAndSO32GUT}{Tadpole cancellation and SO(32)-GUT}}. From this the O$p^-$-brane charge for $p \leq n$ follows from [[T-duality]] (as \hyperlink{TDualityWithTypeIStringTheory}{above}) with respect to [[KK-compactification]] on a [[n-torus|d-torus]] $\mathbb{T}^d$ with $\mathbb{Z}_2$-[[action]] given by canonical [[coordinate function|coordinate]] [[reflection]] \begin{displaymath} \itexarray{ \mathbb{Z}_2 \times \mathbb{R}^{10-d-1,1} \times \mathbb{T}^d &\longrightarrow& \mathbb{R}^{10-d-1,1} \times \mathbb{T}^d \\ (\sigma, (\vec x, \vec y)) &\mapsto& (\vec x, - \vec y) } \,. \end{displaymath} This results in $O(9-d)^-$-planes with [[worldvolume]] $\mathbb{R}^{10-d-1,1}$. But since the [[orbifold]] $\mathbb{T}^d\sslash \mathbb{Z}_2$ now has $2^d$ [[singularities]] /[[fixed points]] (\href{Riemannian+orbifold#CoordinateReflectionOnNTorus}{this Example}) there are now $2^d$ such $O(9-d)^-$-planes. Since the number of [[D-branes]] does not change under [[T-duality]], the total O-plane charge should be the same as before \begin{displaymath} 2^d \cdot q_{O(9-d)} \;=\; 1 \cdot q_{O9} \;=\; -32 \cdot q_{D9} \;=\; - 2^5 \cdot q_{D9} \end{displaymath} which means that the $O(9-d)^-$-plane charge is \begin{displaymath} q_{O(9-d)^-} \;=\; - 2^{5-d} \cdot q_{D(p-d)} \end{displaymath} or equivalently \begin{equation} q_{O p^-} \;=\; - 2^{ p - 4 } \cdot q_{D p} \label{OpPlaneCharge}\end{equation} (e.g. \hyperlink{IbanezUranga12}{Ibáñez-Uranga 12 (5.52)}, \hyperlink{BlumenhagenLustTheisen13}{Blumenhagen-Lüst-Theisen 13 (10.212)}) In summary, we have the following table of O-plane charges on [[flat orbifolds]]: \begin{tabular}{l|l|l|l} [[O-plane]] species&charge $q_{O p^-}/q_{D p}$&transverse [[n-torus&d-torus]]\\ \hline $O9^-$&$-32$&$\mathbb{T}^0$&$\phantom{1}1$\\ $O8^-$&$-16$&$\mathbb{T}^1$&$\phantom{1}2$\\ $O7^-$&$-\phantom{1}8$&$\mathbb{T}^2$&$\phantom{1}4$\\ $O6^-$&$-\phantom{1}4$&$\mathbb{T}^3$&$\phantom{1}8$\\ $O5^-$&$-\phantom{1}2$&$\mathbb{T}^4$&$16$\\ $O4^-$&$-\phantom{1}1$&$\mathbb{T}^5$&$32$\\ \end{tabular} In particular the [[O4-plane]] has negative unit charge (in [[physical unit|units]] of [[D4]]-[[D-brane charge|brane charge]] $q_{D4}$), so that the total charge of $-32$ here comes entirely from the [[number]] $32 = 2^5$ of [[fixed points]] of the $\mathbb{Z}_2$-[[action]] on $\mathbb{T}^5$. O-plane charges of different dimension may be present $\backslash$begin\{center\} $\backslash$end\{center\} \begin{quote}% graphics grabbed from \hyperlink{Johnson97}{Johnson 97} \end{quote} \hypertarget{WithDiscreteTorsion}{}\paragraph*{{In the presence of discrete torsion}}\label{WithDiscreteTorsion} In the presence of [[discrete torsion]] in the [[B-field]] and/or the [[RR-fields]], this charge structure of orientifold planes on [[flat orbifolds]] gets further modified (\hyperlink{HananyKol00}{Hanany-Kol 00, Sec. 2.1}, see \hyperlink{BergmanGimonSugimoto01}{Bergman-Gimon-Sugimoto 01, Sec. 1}): $\backslash$begin\{center\} $\backslash$begin\{imagefromfile\} ``file\_name'': ``OPlaneChargeWithDiscreteTorsion.jpg'', ``width'': 470 $\backslash$end\{imagefromfile\} $\backslash$end\{center\} \begin{quote}% graphics grabbed from \hyperlink{BergmanGimonSugimoto01}{Bergman-Gimon-Sugimoto 01} \end{quote} (In comparing this last table with the \hyperlink{TableOfOPlaneCharges}{above table}, notice that this shows the Op-plane charge in [[physical unit|units]] of $q_{Dq} \coloneqq 1/2$ as in \eqref{DBraneChargeOnOrbifold}.) \hypertarget{in_differential_equivariant_krtheory}{}\paragraph*{{In differential equivariant KR-theory}}\label{in_differential_equivariant_krtheory} A proposal for a formalization of a much more general formula for O-plane charge, regarded in [[differential K-theory|differential]] [[equivariant K-theory|equivariant]] [[KR-theory]] is briefly in \hyperlink{DistlerFreedMoore09}{Distler-Freed-Moore 09, p. 6}. \hypertarget{DualityWithMTheory}{}\subsubsection*{{Duality with M-Theory}}\label{DualityWithMTheory} The possible O-planes in [[M-theory]] are $MO1$ ($\leftrightarrow$[[M-wave]]), [[MO5]] ($\leftrightarrow$[[M5-brane]]) and [[MO9]] (\hyperlink{HananyKol00}{Hanany-Kol 00 around (3.2)}, \hyperlink{HSS18}{HSS 18, Prop. 4.7}). Under the [[duality between M-theory and type IIA string theory]] the O8-plane is identified with the [[MO9]] of [[Horava-Witten theory]]: $\backslash$begin\{center\} $\backslash$end\{center\} \begin{quote}% graphics grabbed from \hyperlink{GKSTY02}{GKSTY 02, section 3} \end{quote} while the [[O4-plane]] is dual to the [[MO5]] (\hyperlink{Hori98}{Hori 98}, \hyperlink{Gimon98}{Gimon 98, Sec. III}, \hyperlink{AKY98}{AKY 98, Sec. II B}, \hyperlink{HananyKol00}{Hanany-Kol 00, 3.1.1}) $\backslash$begin\{center\} $\backslash$end\{center\} \begin{quote}% graphics grabbed from \hyperlink{Gimon98}{Gimon 98} \end{quote} and the $O0$ to the MO1 (\hyperlink{HananyKol00}{Hanany-Kol 00 3.3}) \hypertarget{fractional_branes_at_oplanes}{}\subsubsection*{{Fractional branes at O-planes}}\label{fractional_branes_at_oplanes} By the discussion at \emph{\href{NS5-brane#D6BranesEndingOnNS5Branes}{D-branes ending on NS5 branes}\textbf{, a [[black brane|black]] [[D6-brane]] may end on a [[black brane|black]] [[NS5-brane]], and in fact a priori each [[black brane|brane]] [[NS5-brane]] has to be the junction of two [[black brane|black]] [[D6-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, 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} See also at \emph{[[intersecting D-brane models]]} the section \emph{\href{intersecting+D-brane+model#IntersectionOfD6WithO8}{Intersection of D6s with O8s}}. \hypertarget{related_concepts}{}\subsection*{{Related concepts}}\label{related_concepts} \begin{itemize}% \item [[D-brane]] \item [[M-theory lift of gauge enhancement on D6-branes]] \item \href{NS5-brane#NSHalfBranes}{NS5 half-branes} \end{itemize} \hypertarget{references}{}\subsection*{{References}}\label{references} \hypertarget{general}{}\subsubsection*{{General}}\label{general} The term ``orientifold'' originates around \begin{itemize}% \item Jin Dai, R.G. Leigh, [[Joseph Polchinski]], p. 12 of \emph{New Connections Between String Theories}, Mod.Phys.Lett. A4 (1989) 2073-2083 (\href{http://inspirehep.net/record/25758}{spire:25758}) \end{itemize} Other early accounts include \begin{itemize}% \item [[Clifford Johnson]], \emph{Anatomy of a Duality}, Nucl.Phys. B521 (1998) 71-116 (\href{https://arxiv.org/abs/hep-th/9711082}{arXiv:hep-th/9711082}) \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 [[Edward Witten]], section 5 of \emph{D-branes and K-theory}, J. High Energy Phys., 1998(12):019, 1998 (\href{http://arxiv.org/abs/hep-th/9810188}{arXiv:hep-th/9810188}) \item [[Sunil Mukhi]], Nemani V. Suryanarayana, \emph{Gravitational Couplings, Orientifolds and M-Planes}, JHEP 9909 (1999) 017 (\href{https://arxiv.org/abs/hep-th/9907215}{arXiv:hep-th/9907215}) \item Yoshifumi Hyakutake, Yosuke Imamura, [[Shigeki Sugimoto]], \emph{Orientifold Planes, Type I Wilson Lines and Non-BPS D-branes}, JHEP 0008 (2000) 043 (\href{https://arxiv.org/abs/hep-th/0007012}{arXiv:hep-th/0007012}) \item [[Jan de Boer]], [[Robbert Dijkgraaf]], [[Kentaro Hori]], [[Arjan Keurentjes]], [[John Morgan]], [[David Morrison]], [[Savdeep Sethi]], section 3 of \emph{Triples, Fluxes, and Strings}, Adv.Theor.Math.Phys. 4 (2002) 995-1186 (\href{https://arxiv.org/abs/hep-th/0103170}{arXiv:hep-th/0103170}) \end{itemize} Textbook accounts: \begin{itemize}% \item [[Luis Ibáñez]], [[Angel Uranga]], section 10 of \emph{[[String Theory and Particle Physics -- An Introduction to String Phenomenology]]}, Cambridge 2012 \item [[Ralph Blumenhagen]], [[Dieter Lüst]], [[Stefan Theisen]], Section 9.4 and 10.6 of \emph{Basic Concepts of String Theory} Part of the series Theoretical and Mathematical Physics, Springer 2013 \end{itemize} See also \begin{itemize}% \item Wikipedia, \emph{\href{https://en.wikipedia.org/wiki/Orientifold}{Orientifold}} \end{itemize} \hypertarget{with_discrete_torsion}{}\subsubsection*{{With discrete torsion}}\label{with_discrete_torsion} O-Plane charge in the presence of [[discrete torsion]]: \begin{itemize}% \item \hyperlink{HananyKol00}{Hanany-Kol 00} \item [[Oren Bergman]], [[Eric Gimon]], [[Shigeki Sugimoto]], \emph{Orientifolds, RR Torsion, and K-theory}, JHEP 0105:047, 2001 (\href{https://arxiv.org/abs/hep-th/0103183}{arXiv:hep-th/0103183}) \item Atish Dabholkar, Jaemo Park, \emph{Strings on Orientifolds}, Nucl. Phys. B477 (1996) 701-714 (\href{https://arxiv.org/abs/hep-th/9604178}{arXiv:hep-th/9604178}) \end{itemize} \hypertarget{in_terms_of_kotheory}{}\subsubsection*{{In terms of KO-theory}}\label{in_terms_of_kotheory} O-Plane charge in [[differential K-theory|differential]] [[equivariant K-theory|equivariant]] [[KR-theory]]: \begin{itemize}% \item [[Charles Doran]], Stefan Mendez-Diez, [[Jonathan Rosenberg]], \emph{T-duality For Orientifolds and Twisted KR-theory} (\href{http://arxiv.org/abs/1306.1779}{arXiv:1306.1779}) \item [[Jacques Distler]], [[Dan Freed]], [[Greg Moore]], \emph{Orientifold Pr\'e{}cis} in: [[Hisham Sati]], [[Urs Schreiber]] (eds.) \emph{[[schreiber:Mathematical Foundations of Quantum Field and Perturbative String Theory]]} Proceedings of Symposia in Pure Mathematics, AMS (2011) (\href{http://arxiv.org/abs/0906.0795}{arXiv:0906.0795}, \href{http://www.ma.utexas.edu/users/dafr/bilbao.pdf}{slides}) \item [[Jacques Distler]], [[Dan Freed]], [[Greg Moore]], \emph{Spin structures and superstrings} (\href{http://arxiv.org/abs/1007.4581}{arXiv:1007.4581}) \end{itemize} reviewed/surveyed in \begin{itemize}% \item [[Daniel Freed]], \emph{Dirac charge quantiation, K-theory, and orientifolds}, talk at a workshop \emph{Mathematical methods in general relativity and quantum field theories}, Paris, November 2009 (\href{http://www.ma.utexas.edu/users/dafr/paris_nt.pdf}{pdf}, [[FreedK09.pdf:file]]) \item [[Greg Moore]], \emph{The RR-charge of an orientifold}, Oberwolfach talk 2010 (\href{https://www.physics.rutgers.edu/~gmoore/Oberwolfach_June2010_FINAL.pdf}{pdf}, [[MooreOrientifold2010.pdf:file]], \href{http://www.physics.rutgers.edu/~gmoore/AnnArbor_Feb2010_FINAL.ppt}{ppt}) \item [[Daniel Freed]], \emph{Lectures on twisted K-theory and orientifolds}, lecures at \emph{\href{http://www.esi.ac.at/activities/events/2012/k-theory-and-quantum-fields}{K-Theory and Quantum Fields}}, ESI 2012 ([[FreedESI2012.pdf:file]]) \end{itemize} Actual construction of [[twisted K-theory|twisted]] [[differential K-theory|differential]] [[KO-theory|orthogonal]] [[topological K-theory|K-theory]] and its relation to [[D-brane charge]] in [[type I string theory]] (on [[orientifolds]]): \begin{itemize}% \item Daniel Grady, [[Hisham Sati]], \emph{Twisted differential KO-theory} (\href{https://arxiv.org/abs/1905.09085}{arXiv:1905.09085}) \end{itemize} \hypertarget{examples__models}{}\subsubsection*{{Examples / Models}}\label{examples__models} The [[Witten-Sakai-Sugimoto model]] for [[QCD]] on O-planes: \begin{itemize}% \item Toshiya Imoto, [[Tadakatsu Sakai]], [[Shigeki Sugimoto]], \emph{$O(N)$ and $USp(N)$ QCD from String Theory}, Prog.Theor.Phys.122:1433-1453, 2010 (\href{https://arxiv.org/abs/0907.2968}{arXiv:0907.2968}) \end{itemize} \hypertarget{lift_to_mtheory}{}\subsubsection*{{Lift to M-theory}}\label{lift_to_mtheory} Lift to [[M-theory]] ([[MO5]], [[MO9]]): \begin{itemize}% \item [[Kentaro Hori]], \emph{Consistency Conditions for Fivebrane in M Theory on $\mathbb{R}^5/\mathbb{Z}_2$ Orbifold}, Nucl.Phys.B539:35-78, 1999 (\href{https://arxiv.org/abs/hep-th/9805141}{arXiv:hep-th/9805141}) \item [[Eric Gimon]], \emph{On the M-theory Interpretation of Orientifold Planes} (\href{https://arxiv.org/abs/hep-th/9806226}{arXiv:hep-th/9806226}, \href{http://inspirehep.net/record/472499}{spire:472499}) \item Changhyun Ahn, Hoil Kim, Hyun Seok Yang, \emph{$SO(2N)$ $(0,2)$ SCFT and M Theory on $AdS_7 \times \mathbb{R}P^4$}, Phys.Rev. D59 (1999) 106002 (\href{https://arxiv.org/abs/hep-th/9808182}{arXiv:hep-th/9808182}) \item E. Gorbatov, V.S. Kaplunovsky, J. Sonnenschein, [[Stefan Theisen]], S. Yankielowicz, section 3 of \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 [[Amihay Hanany]], [[Barak Kol]], \emph{On Orientifolds, Discrete Torsion, Branes and M Theory}, JHEP 0006 (2000) 013 (\href{https://arxiv.org/abs/hep-th/0003025}{arXiv:hep-th/0003025}) \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}) \item [[John Huerta]], [[Hisham Sati]], [[Urs Schreiber]], \emph{[[schreiber:Equivariant homotopy and super M-branes|Real ADE-equivariant (co)homotopy and Super M-branes]]} (\href{https://arxiv.org/abs/1805.05987}{arXiv:1805.05987}) \end{itemize} The [[brane intersection|intersection]] with [[(p,q)5-brane webs]]: \begin{itemize}% \item Hirotaka Hayashi, Sung-Soo Kim, Kimyeong Lee, Masato Taki, Futoshi Yagi, \emph{More on 5d descriptions of 6d SCFTs}, JHEP10 (2016) 126 (\href{https://arxiv.org/abs/1512.08239}{arXiv:1512.08239}) \item [[Amihay Hanany]], [[Alberto Zaffaroni]], \emph{Issues on Orientifolds: On the brane construction of gauge theories with $SO(2n)$ global symmetry}, JHEP 9907 (1999) 009 (\href{https://arxiv.org/abs/hep-th/9903242}{arXiv:hep-th/9903242}) \item Gabi Zafrir, \emph{Brane webs in the presence of an $O5^-$-plane and 4d class S theories of type D}, JHEP07 (2016) 035 (\href{https://arxiv.org/abs/1602.00130}{arXiv:1602.00130}) \end{itemize} [[!redirects orientifold planes]] [[!redirects O-plane]] [[!redirects O-planes]] [[!redirects O6-plane]] [[!redirects O6-planes]] [[!redirects O7-plane]] [[!redirects O7-planes]] [[!redirects O8-plane]] [[!redirects O8-planes]] [[!redirects Op-plane]] [[!redirects Op-planes]] [[!redirects O-plane charge]] [[!redirects O-plane charges]] \end{document}