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\begin{document}

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\section*{conformal bootstrap}

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

\hypertarget{algebraic_quantum_field_theory}{}\paragraph*{{Algebraic Quantum Field Theory}}\label{algebraic_quantum_field_theory}

[[!include AQFT and operator algebra contents]]

\hypertarget{contents}{}\section*{{Contents}}\label{contents}

\noindent\hyperlink{idea}{Idea}\dotfill \pageref*{idea} \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{ReferencesSuperconformal}{Superconformal bootstrap}\dotfill \pageref*{ReferencesSuperconformal} \linebreak
\noindent\hyperlink{in_adscft}{In AdS/CFT}\dotfill \pageref*{in_adscft} \linebreak


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

The \emph{conformal bootstrap program} (\hyperlink{BelavinPolyakovZamolofchikov84}{Belavin-Polyakov-Zamolofchikov 84}) is an attempt to construct and classify [[conformal field theories]] [[non-perturbative field theory|non-perturbatively]] by [[axiom|axiomatizing]] the properties of their [[operator product expansion]]/[[correlation functions]].

The conformal bootstrap was proposed in the 1970s as a strategy for calculating the properties of second-order [[phase transitions]]. After spectacular success elucidating two-dimensional systems, little progress was made on systems in higher dimensions until a recent renaissance beginning in 2008 (\hyperlink{PolandSimmonsDuffin16}{Poland-Simmons-Duffin 16}).

The generalization of the conformal bootstrap to [[superconformal field theories]] has the potential to provide, via [[AdS/CFT]], a precise and detailed construction of [[large-N limit|large-N]] and [[asymptotic boundary|asymptotically]] [[anti-de Sitter spacetime|AdS]] [[string theory|string]]/[[M-theory]].

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

\begin{itemize}%
\item [[Wightman axioms]], [[conformal net]]

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

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

\begin{itemize}%
\item [[Alexander Belavin]], [[Alexander Polyakov]], [[Alexander Zamolodchikov]], (1984). \emph{Infinite conformal symmetry in two-dimensional quantum field theory}. Nuclear Physics B. 241 (2): 333--380 (1984)


\item [[David Poland]], [[David Simmons-Duffin]], \emph{The conformal bootstrap}, Nature Physics 535--539 (2016) \href{http://www.nature.com.edgesuite.net/nphys/journal/v12/n6/full/nphys3761.html}{doi:10.1038/nphys3761}


\item [[David Simmons-Duffin]], \emph{TASI Lectures on the Conformal Bootstrap} (\href{https://arxiv.org/abs/1602.07982}{arXiv:1602.07982})


\item David Poland, Slava Rychkov, Alessandro Vichi, \emph{The Conformal Bootstrap: Numerical Techniques and Applications} (\href{https://arxiv.org/abs/1805.04405}{arXiv:1805.04405})


\item Shai M. Chester, \emph{Weizmann Lectures on the Numerical Conformal Bootstrap} (\href{https://arxiv.org/abs/1907.05147}{arXiv:1907.05147})



\end{itemize}
See also

\begin{itemize}%
\item Wikipedia, \emph{\href{https://en.wikipedia.org/wiki/Conformal_bootstrap}{Conformal bootstrap}}

\end{itemize}
\hypertarget{ReferencesSuperconformal}{}\subsubsection*{{Superconformal bootstrap}}\label{ReferencesSuperconformal}

For [[superconformal field theory]], such as [[D=4 N=1 SYM]], [[D=4 N=2 SYM]], [[D=4 N=4 SYM]], [[D=6 N=(1,0) SCFT]], [[D=6 N=(2,0) SCFT]]:

\begin{itemize}%
\item [[Christopher Beem]], Madalena Lemos, Pedro Liendo, [[Leonardo Rastelli]], Balt C. van Rees, \emph{The $N=2$ superconformal bootstrap} (\href{https://arxiv.org/abs/1412.7541}{arXiv:1412.7541})


\item [[Christopher Beem]], Madalena Lemos, [[Leonardo Rastelli]], Balt C. van Rees, \emph{The $(2,0)$ superconformal bootstrap} (\href{https://arxiv.org/abs/1507.05637}{arXiv:1507.05637})


\item [[Christopher Beem]], [[Leonardo Rastelli]], Balt C. van Rees, \emph{More $N=4$ superconformal bootstrap} (\href{https://arxiv.org/abs/1612.02363}{arXiv:1612.02363})



\end{itemize}
\hypertarget{in_adscft}{}\subsubsection*{{In AdS/CFT}}\label{in_adscft}

Discussion of [[superconformal bootstrap]] in view of [[AdS/CFT]], hence as a precise and detailed construction of [[large-N limit|large-N]] and [[asymptotic boundary|asymptotically]] [[anti-de Sitter spacetime|AdS]] [[string theory]]/[[M-theory]]:

[[KK-compactification|extra dimensions]]:

\begin{itemize}%
\item [[Luis Alday]], [[Eric Perlmutter]], \emph{Growing Extra Dimensions in AdS/CFT} (\href{https://arxiv.org/abs/1906.01477}{arXiv1906.01477})

\end{itemize}
[[string scattering amplitudes]] ;

\begin{itemize}%
\item [[Luis Alday]], [[Agnese Bissi]], [[Eric Perlmutter]], \emph{Genus-One String Amplitudes from Conformal Field Theory}, JHEP06(2019) 010 (\href{https://arxiv.org/abs/1809.10670}{arXiv:1809.10670})

\end{itemize}
The [[D=6 N=(2,0) SCFT]] on the [[M5-brane]]:

\begin{itemize}%
\item Shai M. Chester, [[Eric Perlmutter]], \emph{M-Theory Reconstruction from $(2,0)$ CFT and the Chiral Algebra Conjecture}, J. High Energ. Phys. (2018) 2018: 116 (\href{https://arxiv.org/abs/1805.00892}{arXiv:1805.00892})

from p. 2:

\begin{quote}%
On the other hand, given our utter lack of a complete description of M-theory, the bulk is not terribly useful for determining finite aspects of the dual CFT. However, we can turn this problem around using the modern perspective of the conformal bootstrap, which gives an a priori independent formulation of the (local sector of the) CFT. This provides an independent tool for constructing M-theory at the non-perturbative level, a philosophy that we will substantiate in this work.


\end{quote}


\end{itemize}
The [[D=3 SCFT]] ([[BLG-model]], [[ABJM model]]) on the [[M2-brane]]:

\begin{itemize}%
\item Nathan B. Agmon, Shai M. Chester, Silviu S. Pufu, \emph{The M-theory Archipelago} (\href{https://arxiv.org/abs/1907.13222}{arXiv:1907.13222})

\end{itemize}
[[!redirects conformal bootstrap program]]

[[!redirects superconformal bootstrap]]



\end{document}