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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*{D=6 N=(2,0) SCFT} \hypertarget{context}{}\subsubsection*{{Context}}\label{context} \hypertarget{quantum_field_theory}{}\paragraph*{{Quantum field theory}}\label{quantum_field_theory} [[!include functorial quantum field theory - contents]] \hypertarget{supergeometry}{}\paragraph*{{Super-Geometry}}\label{supergeometry} [[!include supergeometry - contents]] \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{GeometricEngineering}{Geometric engineering}\dotfill \pageref*{GeometricEngineering} \linebreak \noindent\hyperlink{holographic_dual}{Holographic dual}\dotfill \pageref*{holographic_dual} \linebreak \noindent\hyperlink{realization_of_quantum_chromodynamics}{Realization of quantum chromodynamics}\dotfill \pageref*{realization_of_quantum_chromodynamics} \linebreak \noindent\hyperlink{solitonic_1branes}{Solitonic 1-branes}\dotfill \pageref*{solitonic_1branes} \linebreak \noindent\hyperlink{CompactificationOnARiemannSurface}{Compactification on a Riemann surface and AGT correspondence}\dotfill \pageref*{CompactificationOnARiemannSurface} \linebreak \noindent\hyperlink{twistor_space_description}{Twistor space description}\dotfill \pageref*{twistor_space_description} \linebreak \noindent\hyperlink{related_entries}{Related entries}\dotfill \pageref*{related_entries} \linebreak \noindent\hyperlink{references}{References}\dotfill \pageref*{references} \linebreak \noindent\hyperlink{general}{General}\dotfill \pageref*{general} \linebreak \noindent\hyperlink{compactification_to_5d_superyangmills}{Compactification to 5d super-Yang-Mills}\dotfill \pageref*{compactification_to_5d_superyangmills} \linebreak \noindent\hyperlink{compactification_to_4d_superyangmills}{Compactification to 4d super-Yang-Mills}\dotfill \pageref*{compactification_to_4d_superyangmills} \linebreak \noindent\hyperlink{ade_classification}{ADE classification}\dotfill \pageref*{ade_classification} \linebreak \noindent\hyperlink{ModelsAndSpecialProperties}{Models and special properties}\dotfill \pageref*{ModelsAndSpecialProperties} \linebreak \noindent\hyperlink{ReferencesOnTheHolographicDual}{On the holographic dual}\dotfill \pageref*{ReferencesOnTheHolographicDual} \linebreak \noindent\hyperlink{solitonic_1brane_excitations}{Solitonic 1-brane excitations}\dotfill \pageref*{solitonic_1brane_excitations} \linebreak \noindent\hyperlink{extended_tqft_and_quantum_anomalies}{Extended TQFT and quantum anomalies}\dotfill \pageref*{extended_tqft_and_quantum_anomalies} \linebreak \hypertarget{idea}{}\subsection*{{Idea}}\label{idea} According to the \href{supersymmetry#ClassificationSuperconformal}{classification of superconformal symmetry}, there should exists [[superconformal field theories]] in 6 dimensions\ldots{} [[!include superconformal symmetry -- table]] \ldots{}with $(2,0)$-[[supersymmetry]], that contain a [[self-dual higher gauge theory]] whose field configurations are [[connections on a 2-bundle]] (a [[circle n-bundle with connection|circle 2-bundle with connection]] in the abelian case). In (\hyperlink{ClausKalloshProeyen97}{Claus-Kallosh-Proeyen 97}) such has been derived, in the abelian case and to low order, as the small fluctuations of the [[Green-Schwarz sigma-model]] of the [[M5-brane]] around the embedding in the [[asymptotic boundary]] of the [[AdS-spacetime]] that is the [[near-horizon geometry]] of the [[black brane|black]] M5-brane. In accord with this the \href{AdS-CFT#AdS7CFT6}{AdS7-CFT6} correspondence predicts that the nonabelian 6d theory is the corresponding theory for $N$ coincident M5-branes. In the non-abelian case this is expected (\hyperlink{Witten07}{Witten 07}) that the compactification of such theories are at the heart of the phenomenon that leads to [[S-duality]] in [[super Yang-Mills theory]] and further to [[geometric Langlands duality]] (\hyperlink{Witten09}{Witten 09}). Due to the [[self-dual higher gauge theory|self-duality]] a characterization of these theories by an [[action functional]] is subtle. Therefore more direct descriptions are still under investigation (for instance \hyperlink{SSW11}{SSW11}). A review of recent developments is in (\hyperlink{Moore}{Moore11}). \hypertarget{properties}{}\subsection*{{Properties}}\label{properties} \hypertarget{GeometricEngineering}{}\subsubsection*{{Geometric engineering}}\label{GeometricEngineering} For [[geometric engineering]] of the [[6d (2,0)-superconformal QFT]], see at \emph{\href{duality+between+M-theory+on+Z2-orbifolds+and+type+IIB+string+theory+on+K3-fibrations#GeometricEngineeringOfThe6d2SuperconformalQFT}{duality between M-theory on Z2-orbifolds and type IIB string theory on K3-fibrations -- Geometric engineering of 6d (2,0)-SCFT}}. \hypertarget{holographic_dual}{}\subsubsection*{{Holographic dual}}\label{holographic_dual} Under [[AdS-CFT|AdS7/CFT6]] the 6d $(2,0)$-superconformal QFT is supposed to be dual to [[11-dimensional supergravity|M-theory]] on [[anti de Sitter spacetime]] $AdS_7 \times S^4$. See [[AdS/CFT correspondence]] for more on this. \hypertarget{realization_of_quantum_chromodynamics}{}\subsubsection*{{Realization of quantum chromodynamics}}\label{realization_of_quantum_chromodynamics} See at \emph{[[AdS-QCD correspondence]]}. \hypertarget{solitonic_1branes}{}\subsubsection*{{Solitonic 1-branes}}\label{solitonic_1branes} The 5d $(2,0)$-[[SCFT]] has tensionless 1-[[brane]] configurations. From the point of view of the ambient [[11-dimensional supergravity]] these are the boundaries of [[M2-branes]] ending on the [[M5-branes]]. (\hyperlink{GGT}{GGT}) \hypertarget{CompactificationOnARiemannSurface}{}\subsubsection*{{Compactification on a Riemann surface and AGT correspondence}}\label{CompactificationOnARiemannSurface} $\backslash$begin\{imagefromfile\} ``file\_name'': ``6d\_qft\_graph.gif'', ``width'': 600, ``float'': ``right'', ``margin'': \{ ``top'': 0, ``right'': 20, ``bottom'': 10, ``left'': 20, ``unit'': ``px'' \}, ``alt'': ``Compactification diagram'' $\backslash$end\{imagefromfile\} \begin{quote}% (graphics taken from (\hyperlink{Workshop14}{Workshop 14})) \end{quote} The [[Kaluza-Klein mechanism|compactification]] of the 5-brane on a [[Riemann surface]] yields as [[worldvolume]] [[theory (physics)|theory]] [[N=2 D=4 super Yang-Mills theory]]. See at \emph{\href{N%3D2+D%3D4+super+Yang-Mills+theory#ConstructionByCompactificationOf5Branes}{N=2 D=4 SYM -- Construction by compactification of 5-branes}}. The \emph{[[AGT correspondence]]} relates the [[partition function]] of $SU(2)^{n+3g-3}$-[[N=2 D=4 super Yang-Mills theory]] obtained by [[Kaluza-Klein mechanism|compactifying]] the $6d$ M5-brane theory on a [[Riemann surface]] $C_{g,n}$ of [[genus]] $g$ with $n$ punctures to 2d [[Liouville theory]] on $C_{g,n}$. More generally, this kind of construction allows to describe the 6d (2,0)-theory as a ``[[2d SCFT]] with values in [[super Yang-Mills theory|4d SYM]]''. See at \emph{[[AGT correspondence]]} for more on this. \hypertarget{twistor_space_description}{}\subsubsection*{{Twistor space description}}\label{twistor_space_description} Famously the solutions to [[self-dual Yang-Mills theory]] in [[dimension]] 4 can be obtained as images of degree-2 cohomology classes under the [[Penrose-Ward twistor transform]]. Since the 6d QFT on the [[M5-brane]] contains a 2-form [[self-dual higher gauge field]] it seems natural to expect that it can be described by a higher analogy of the twistor transform. For references exploring this idea see at \emph{\href{twistor+space#ReferencesApplicationToSelfDual2FormField}{twistor space -- References -- Application to the self-dual 2-form field in 6d}}. \hypertarget{related_entries}{}\subsection*{{Related entries}}\label{related_entries} \begin{itemize}% \item [[little string theory]] \item [[D=6 N=(1,0) SCFT]] \item [[D=6 supergravity]] \item [[D=2 N=(2,0) SCFT]] \item [[D=5 super Yang-Mills theory]] \end{itemize} [[!include gauge theory from AdS-CFT -- table]] [[!include superconformal symmetry -- table]] \hypertarget{references}{}\subsection*{{References}}\label{references} \hypertarget{general}{}\subsubsection*{{General}}\label{general} The first indication of a 6d theory with a self-dual 2-form field appears in \begin{itemize}% \item [[Edward Witten]], section 1 of \emph{Some comments on string dynamics} (\href{http://arxiv.org/abs/hep-th/9507121}{hepth/9507121}) \end{itemize} Derivation of the abelian 6d theory to low order as the small fluctuations of the [[Green-Schwarz sigma-model]] of the [[M5-brane]] around a solution embedding as the asymptotic boundary of the [[AdS-spacetime]] [[near-horizon geometry]] of a [[black brane|black]] 5-brane is due to \begin{itemize}% \item P. Claus, [[Renata Kallosh]], [[Antoine Van Proeyen]], \emph{M 5-brane and superconformal $(0,2)$ tensor multiplet in 6 dimensions}, Nucl.Phys. B518 (1998) 117-150 (\href{http://arxiv.org/abs/hep-th/9711161}{arXiv:hep-th/9711161}) \end{itemize} General survey includes \begin{itemize}% \item [[Greg Moore]], \emph{On the role of sixdimensional $(2,0)$-theories in recent developments in Physical Mathematics}, talk at \href{http://www2.physics.uu.se/external/strings2011/}{Strings 2011} (\href{http://www.physics.rutgers.edu/~gmoore/Strings2011FinalPDF.pdf}{pdf slides}) \item [[Greg Moore]], \emph{Applications of the six-dimensional (2,0) theories to Physical Mathematics}, \href{http://www.hcm.uni-bonn.de/events/eventpages/felix-klein-lectures/applications-of-the-six-dimensional-20-theories-to-physical-mathematics/}{Felix Klein lectures Bonn (2012)} (\href{http://www.physics.rutgers.edu/~gmoore/FelixKleinLectureNotes.pdf}{pdf}, [[MooreKleinLectures12.pdf:file]]) \item [[Qiaochu Yuan]]: \emph{\href{https://math.berkeley.edu/~qchu/Notes/6d/}{lecture notes}} for \emph{\href{http://www.math.northwestern.edu/~celliott/workshop/}{Mathematical Aspects of Six-Dimensional Quantum Field Theories}}, Berkeley, December 8th-12th, 2014 at the University of California, Berkeley \end{itemize} Construction from [[F-theory]] [[KK-compactification]] is reviewed in \begin{itemize}% \item [[Jonathan Heckman]], [[Tom Rudelius]], \emph{Top Down Approach to 6D SCFTs}, J. Phys. A: Math. Theor. 52 093001 2018 (\href{https://arxiv.org/abs/1805.06467}{arXiv:1805.06467}, \href{https://doi.org/10.1088/1751-8121/aafc81}{doi:10.1088/1751-8121/aafc81}) \end{itemize} See also the references and discussion at \emph{[[M5-brane]]}. \hypertarget{compactification_to_5d_superyangmills}{}\subsubsection*{{Compactification to 5d super-Yang-Mills}}\label{compactification_to_5d_superyangmills} [[KK-compactification]] on [[circle]] [[fibers]] to [[D=5 super Yang-Mills theory]] is discussed in (see also at [[Perry-Schwarz Lagrangian]]): \begin{itemize}% \item [[Nathan Seiberg]], Sec. 7 of \emph{Notes on Theories with 16 Supercharges}, Nucl. Phys. Proc. Suppl. 67:158-171, 1998 (\href{https://arxiv.org/abs/hep-th/9705117}{arXiv:hep-th/9705117}) \item [[Michael Douglas]], \emph{On D=5 super Yang-Mills theory and (2,0) theory}, JHEP 1102:011, 2011 (\href{https://arxiv.org/abs/1012.2880}{arXiv:1012.2880}) \item [[Neil Lambert]], Constantinos Papageorgakis, Maximilian Schmidt-Sommerfeld, \emph{M5-Branes, D4-Branes and Quantum 5D super-Yang-Mills}, JHEP 1101:083, 2011 (\href{https://arxiv.org/abs/1012.2882}{arXiv:1012.2882}) \item [[Edward Witten]], Sections 4 and 5 of \emph{Fivebranes and Knots} (\href{http://arxiv.org/abs/1101.3216}{arXiv:1101.3216}) \item [[Chris Hull]], [[Neil Lambert]], \emph{Emergent Time and the M5-Brane}, JHEP06(2014)016 (\href{https://arxiv.org/abs/1403.4532}{arXiv:1403.4532}) \item [[Andreas Gustavsson]], \emph{Five-dimensional Super-Yang-Mills and its Kaluza-Klein tower}. JHEP01(2019)222 (\href{https://arxiv.org/abs/1812.01897}{arXiv:1812.01897}) \item [[Neil Lambert]], Sec. 3.1 and 3.4.3. of \emph{Lessons from M2's and Hopes for M5's}, \emph{Proceedings of the \href{http://www.maths.dur.ac.uk/lms/}{LMS-EPSRC Durham Symposium}:} \emph{\href{http://www.maths.dur.ac.uk/lms/109/index.html}{Higher Structures in M-Theory}, August 2018} Fortschritte der Physik, 2019 (\href{https://arxiv.org/abs/1903.02825}{arXiv:1903.02825}, \href{http://www.maths.dur.ac.uk/lms/109/talks/1877lambert.pdf}{slides pdf}) \end{itemize} \hypertarget{compactification_to_4d_superyangmills}{}\subsubsection*{{Compactification to 4d super-Yang-Mills}}\label{compactification_to_4d_superyangmills} [[KK-compactification]] on [[torus]] [[fibers]] to [[D=4 super Yang-Mills theory]] and the related [[electric-magnetic duality]]/[[S-duality]] in 4-dimensions is discussed in \begin{itemize}% \item [[Edward Witten]], \emph{[[Conformal field theory in four and six dimensions]]} in [[Ulrike Tillmann]] (ed.) \emph{Topology, geometry and quantum field theory} LMS Lecture Note Series (2004) (\href{http://arxiv.org/abs/0712.0157}{arXiv:0712.0157}) \end{itemize} and the resulting relation to the [[geometric Langlands correspondence]] is disucssed in \begin{itemize}% \item [[Edward Witten]], \emph{Geometric Langlands From Six Dimensions}, in Peter Kotiuga (ed.) \emph{A Celebration of the Mathematical Legacy of Raoul Bott}, AMS 2010 (\href{http://arxiv.org/abs/0905.2720}{arXiv:0905.2720}) \end{itemize} For more references on this see at \emph{[[N=2 D=4 super Yang-Mills theory]]} the section \emph{\href{N%3D2+D%3D4+super+Yang-Mills+theory#ConstructionByCompactificationOf5Branes}{References - Constructions from 5-branes}}. Relation to [[BFSS matrix model]] on tori: \begin{itemize}% \item [[Micha Berkooz]], [[Moshe Rozali]], [[Nathan Seiberg]], \emph{Matrix Description of M-theory on $T^3$ and $T^5$} (\href{http://arxiv.org/abs/hep-th/9704089}{arXiv:hep-th/9704089}) \end{itemize} The [[KK-compactification]] specifically of the [[D=6 N=(1,0) SCFT]] to [[D=4 N=1 super Yang-Mills]]: \begin{itemize}% \item Ibrahima Bah, Christopher Beem, Nikolay Bobev, Brian Wecht, \emph{Four-Dimensional SCFTs from M5-Branes} (\href{http://arxiv.org/abs/1203.0303}{arXiv:1203.0303}) \item Shlomo S. Razamat, [[Cumrun Vafa]], Gabi Zafrir, \emph{$4d$ $\mathcal{N} = 1$ from $6d (1,0)$}, J. High Energ. Phys. (2017) 2017: 64 (\href{https://arxiv.org/abs/1610.09178}{arXiv:1610.09178}) \item Ibrahima Bah, [[Amihay Hanany]], Kazunobu Maruyoshi, Shlomo S. Razamat, Yuji Tachikawa, Gabi Zafrir, \emph{$4d$ $\mathcal{N}=1$ from $6d$ $\mathcal{N}=(1,0)$ on a torus with fluxes} (\href{https://arxiv.org/abs/1702.04740}{arXiv:1702.04740}) \item Hee-Cheol Kim, Shlomo S. Razamat, [[Cumrun Vafa]], Gabi Zafrir, \emph{E-String Theory on Riemann Surfaces}, Fortsch. Phys. (\href{https://arxiv.org/abs/1709.02496}{arXiv:1709.02496}) \item Hee-Cheol Kim, Shlomo S. Razamat, [[Cumrun Vafa]], Gabi Zafrir, \emph{D-type Conformal Matter and SU/USp Quivers}, JHEP06(2018)058 (\href{https://arxiv.org/abs/1802.00620}{arXiv:1802.00620}) \item Hee-Cheol Kim, Shlomo S. Razamat, [[Cumrun Vafa]], Gabi Zafrir, \emph{Compactifications of ADE conformal matter on a torus}, JHEP09(2018)110 (\href{https://arxiv.org/abs/1806.07620}{arXiv:1806.07620}) \item Shlomo S. Razamat, Gabi Zafrir, \emph{Compactification of 6d minimal SCFTs on Riemann surfaces}, Phys. Rev. D 98, 066006 (2018) (\href{https://arxiv.org/abs/1806.09196}{arXiv:1806.09196}) \item Jin Chen, Babak Haghighat, Shuwei Liu, Marcus Sperling, \emph{4d N=1 from 6d D-type N=(1,0)} (\href{https://arxiv.org/abs/1907.00536}{arXiv:1907.00536}) \end{itemize} \hypertarget{ade_classification}{}\subsubsection*{{ADE classification}}\label{ade_classification} Discussion of the [[ADE classification]] of the 6d theories includes, after (\hyperlink{Witten95}{Witten95}) \begin{itemize}% \item Julie D. Blum, [[Kenneth Intriligator]], \emph{New Phases of String Theory and 6d RG Fixed Points via Branes at Orbifold Singularities}, Nucl.Phys.B506:199-222,1997 (\href{http://arxiv.org/abs/hep-th/9705044}{arXiv:hep-th/9705044}) \item [[Jonathan Heckman]], [[David Morrison]], [[Cumrun Vafa]], \emph{On the Classification of 6D SCFTs and Generalized ADE Orbifolds} (\href{http://arxiv.org/abs/1312.5746}{arXiv:1312.5746}) \end{itemize} \hypertarget{ModelsAndSpecialProperties}{}\subsubsection*{{Models and special properties}}\label{ModelsAndSpecialProperties} Realization of the 6d theory in [[F-theory]] is discussed in (\hyperlink{HeckmannMorrisonVafa13}{Heckmann-Morrison-Vafa 13}). A proposal for related higher nonabelian differential form data is made in \begin{itemize}% \item [[Henning Samtleben]], Ergin Sezgin, Robert Wimmer, \emph{(1,0) superconformal models in six dimensions} (\href{http://arxiv.org/abs/1108.4060}{arXiv:1108.4060}) \end{itemize} Since by [[transgression]] every nonabelian [[principal 2-bundle]]/[[gerbe]] gives rise to some kind of nonabelian 1-bundle on [[loop space]] it is clear that some parts (but not all) of the nonabelian gerbe theory on the 5-brane has an equivalent reformulation in terms of ordinary gauge theory on the [[loop space]] of the 5-brane and possibly for gauge group the [[loop group]] of the original gauge group. Comments along these lines have been made in \begin{itemize}% \item [[Andreas Gustavsson]], \emph{Selfdual strings and loop space Nahm equations} (\href{http://arxiv.org/abs/0802.3456}{arXiv:0802.3456}). \end{itemize} In fact, via the [[strict 2-group]] version of the [[string 2-group]] there is a local gauge in which the loop group variables appear already before transgression of the 5-brane gerbe to loop space. This is discussed from a [[holographic principle|holographic]] point of view in \begin{itemize}% \item [[Domenico Fiorenza]], [[Hisham Sati]], [[Urs Schreiber]], \emph{[[schreiber:7d Chern-Simons theory and the 5-brane]]} \end{itemize} \hypertarget{ReferencesOnTheHolographicDual}{}\subsubsection*{{On the holographic dual}}\label{ReferencesOnTheHolographicDual} The basics of the relation of the 6d theory to a 7d theory under [[AdS-CFT]] is reviewed [[holographic principle|holographic duality]] \begin{itemize}% \item [[Juan Maldacena]], \emph{The Large N limit of superconformal field theories and supergravity}, Adv. Theor. Math. Phys. 2:231, 1998, \href{http://arxiv.org/abs/hep-th/9711200}{hep-th/9711200}; \emph{Wilson loops in Large N field theories}, Phys. Rev. Lett. \textbf{80} (1998) 4859, \href{http://arxiv.org/abs/hep-th/9803002}{hep-th/9803002} \end{itemize} The argument that the abelian [[7d Chern-Simons theory]] of a [[circle n-bundle with connection|3-connection]] yields this way the [[conformal blocks]] of the abelian [[self-dual higher gauge theory]] of the 6d theory on a \emph{single} brane is due to \begin{itemize}% \item [[Edward Witten]], \emph{Five-Brane Effective Action In M-Theory} J. Geom. Phys.22:103-133,1997 (\href{http://arxiv.org/abs/hep-th/9610234}{arXiv:hep-th/9610234}) \item [[Edward Witten]], \emph{AdS/CFT Correspondence And Topological Field Theory} JHEP 9812:012,1998 (\href{http://arxiv.org/abs/hep-th/9812012}{arXiv:hep-th/9812012}) \end{itemize} The nonabelian generalization of this 7d action functional that follows from taking the quantum corrections ([[Green-Schwarz mechanism]] and flux quantization) of the [[supergravity C-field]] into account is discussed in \begin{itemize}% \item [[Domenico Fiorenza]], [[Hisham Sati]], [[Urs Schreiber]], \emph{[[schreiber:7d Chern-Simons theory and the 5-brane]]} \end{itemize} See also \begin{itemize}% \item [[Eric D'Hoker]], John Estes, Michael Gutperle, Darya Krym, \emph{Exact Half-BPS Flux Solutions in M-theory I Local Solutions} (\href{http://arxiv.org/abs/0806.0605}{arXiv:0806.0605}) \emph{Exact Half-BPS Flux Solutions in M-theory II: Global solutions asymptotic to $AdS_7 \times S^4$ (\href{http://arxiv.org/abs/0810.4647}{arXiv:0810.4647})} \end{itemize} \hypertarget{solitonic_1brane_excitations}{}\subsubsection*{{Solitonic 1-brane excitations}}\label{solitonic_1brane_excitations} \begin{itemize}% \item [[Jerome Gauntlett]], [[Joaquim Gomis]], [[Paul Townsend]], \emph{BPS Bounds for Worldvolume Branes} (\href{http://arxiv.org/abs/hep-th/9711205}{arXiv:hep-th/9711205}) \item [[Paul Howe]], [[Neil Lambert]], [[Peter West]], \emph{The Threebrane Soliton of the M-Fivebrane} (\href{http://arxiv.org/abs/hep-th/9710033}{arXiv:hep-th/9710033}) \end{itemize} \hypertarget{extended_tqft_and_quantum_anomalies}{}\subsubsection*{{Extended TQFT and quantum anomalies}}\label{extended_tqft_and_quantum_anomalies} Relation to [[extended TQFT]] and [[quantum anomalies]] (motivated via [[M5-brane]] lore) is discussed in \begin{itemize}% \item [[Dan Freed]], \emph{[[4-3-2 8-7-6]]} \item [[David Ben-Zvi]], \emph{Algebraic geometry of topological field theories}, talk at \emph{\href{https://www.msri.org/workshops/689}{Reimagining the Foundations of Algebraic Topology April 07, 2014 - April 11, 2014}} (\href{https://www.msri.org/workshops/689/schedules/18216}{web video}) \item [[Samuel Monnier]], \emph{The global anomalies of (2,0) superconformal field theories in six dimensions}, JHEP09(2014)088 (\href{https://arxiv.org/abs/1406.4540}{arXiv:1406.4540}) \item [[Samuel Monnier]], \emph{The anomaly field theories of six-dimensional (2,0) superconformal theories} (\href{https://arxiv.org/abs/1706.01903}{arXiv:1706.01903}) \item [[Samuel Monnier]], [[Gregory Moore]], \emph{A Brief Summary Of Global Anomaly Cancellation In Six-Dimensional Supergravity}, (\href{https://arxiv.org/abs/1808.01335}{arXiv:1808.01335}, \end{itemize} a summary of \begin{itemize}% \item [[Samuel Monnier]], [[Gregory Moore]], \emph{Remarks on the Green-Schwarz terms of six-dimensional supergravity theories}, (\href{https://arxiv.org/abs/1808.01334}{arXiv:1808.01334} \end{itemize} [[!redirects 6d (2,0)-susy QFT]] [[!redirects 6d (2,0)-superconformal QFT]] [[!redirects 6d (2,0)-superconformal field theory]] [[!redirects 6d (2,0)-superconformal field theories]] [[!redirects 6d (2,0)-superconformal SCFT]] [[!redirects 6d (2,0)-superconformal SCFTs]] [[!redirects 6d superconformal gauge field theory]] [[!redirects 6d superconformal gauge field theories]] [[!redirects D=6 N=(2,0) SCFT]] [[!redirects D=6 N=(2,0) SCFTs]] [[!redirects D=6 N=(1,1) SCFT]] [[!redirects 6d (2,0)-supersymmetric QFT]] \end{document}