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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*{higher spin gauge theory} \hypertarget{context}{}\subsubsection*{{Context}}\label{context} \hypertarget{physics}{}\paragraph*{{Physics}}\label{physics} [[!include physicscontents]] \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{references}{References}\dotfill \pageref*{references} \linebreak \noindent\hyperlink{general}{General}\dotfill \pageref*{general} \linebreak \noindent\hyperlink{ReferencesRelationToStringTheory}{Relation to string theory}\dotfill \pageref*{ReferencesRelationToStringTheory} \linebreak \noindent\hyperlink{relation_to_other_systems}{Relation to other systems}\dotfill \pageref*{relation_to_other_systems} \linebreak \noindent\hyperlink{higher_spin_chernsimons_theory}{Higher spin Chern-Simons theory}\dotfill \pageref*{higher_spin_chernsimons_theory} \linebreak \noindent\hyperlink{relation_to_holography}{Relation to holography}\dotfill \pageref*{relation_to_holography} \linebreak \hypertarget{idea}{}\subsection*{{Idea}}\label{idea} Generally by a \emph{higher spin field theory} is meant a [[quantum field theory]] that involves [[field (physics)|fields]] of spin $\gt 2$ (recalling that a [[spinor field]] has spin 1/2, a [[gauge field]] has spin 1, a [[gravitino]] field has spin 3/2 and the field of [[gravity]] has spin 2). Folklore had it that all higher spin field theories with \emph{[[mass]]-less} higher spin fields are inconsistent due to negative norm states (``ghost'') appearing in their [[quantization]]. (This argument underlies the dominance of $\mathcal{N} = 1$ [[11-dimensional supergravity]], see the introduction to the entry \emph{[[12-dimensional supergravity]]} for more on this). But then it was discovered that there is a gigher spin gauge theory (\hyperlink{Vasiliev96}{Vasiliev 96}) which is a kind of [[higher gauge theory]] whose [[field (physics)|field content]] is an \emph{infinite tower} of massless fields of ever higher [[spin]]. Ever since the refine folklore says that higher spin theories with a \emph{finite} number of higher spin field species is inconsistent, but that an infinite tower can fix the problem (\ldots{}add reference\ldots{}). One way that higher spin gauge theories are thought to naturally arise is as the limiting case of [[string field theory]] when the [[string tension]] is sent to zero (\hyperlink{HenneauxTeitelboim87}{Henneaux-Teitelboim 87, section 2}, \hyperlink{Gross88}{Gross 88}, \hyperlink{SagnottiTsulaia03}{Sagnotti-Tsulaia 03}, \hyperlink{Bonelli03}{Bonelli 03}): The excitation spectrum of the [[string]] [[sigma-model]] contains beyond the massless particles of the [[effective QFT|effective]] [[supergravity]] theory an infinite tower of massive excitations, of ever higher [[spin]]. There are, however, certain limits in which all these masses become negligible to a reference energy scale -- the \emph{tensionless limit} -- this is notably so for compactifications on [[anti de Sitter spaces]] of small radius. In this limit the string spectrum looks like an infinite collection of massless [[spinning particles]] for ever higher spin. Due to their common origin in the string, these share intricate relations among each other, which are argued to be described by higher spin gauge theory. (Notice that at least closed bosonic [[string field theory]] is itself already a [[higher gauge theory]], even without sending the [[string tension]] to zero, see at \emph{\href{string+field+theory#AsAnInfinityCSTheory}{closed string field theory -- As an ∞-Chern-Simons theory}}.) \hypertarget{references}{}\subsection*{{References}}\label{references} \hypertarget{general}{}\subsubsection*{{General}}\label{general} Original articles include \begin{itemize}% \item [[Mikhail Vasiliev]], \emph{Higher-Spin Gauge Theories in Four, Three and Two Dimensions} (\href{http://arxiv.org/abs/hep-th/9611024}{arXiv:hep-th/9611024}) \end{itemize} Reviews and lecture notes include the following: \begin{itemize}% \item [[Mikhail Vasiliev]], \emph{Higher Spin Gauge Theories in Various Dimensions}, 27th Johns Hopkins Workshop on Current Problems in Particle Theory: Symmetries and Mysteries of M Theory (\href{https://arxiv.org/abs/hep-th/0401177}{arXiv:hep-th/0401177}) \item [[Mikhail Vasiliev]], \emph{Higher spin gauge theories in any dimension} talk at String2004 in Moscow (\href{https://arxiv.org/abs/hep-th/0409260}{arXiv:hep-th/0409260}) \item R. Argurio, [[Glenn Barnich]], G. Bonelli, M. Grigoriev (eds.) \emph{Higher spin gauge theories} Solvay Workshops and Symposia (2004) (\href{http://www.ulb.ac.be/sciences/ptm/pmif/Solvay1proc.pdf}{pdf}) \item [[Xavier Bekaert]], S. Cnockaert, Carlo Iazeolla, [[Mikhail Vasiliev]], \emph{Nonlinear higher spin theories in various dimensions} (\href{https://arxiv.org/abs/hep-th/0503128}{arXiv:0503128}) \item V.E. Didenko, E.D. Skvortsov, \emph{Elements of Vasiliev theory} (\href{https://arxiv.org/abs/1401.2975}{arXiv:1401.2975}) \item Rakibur Rahman, Massimo Taronna, \emph{From Higher Spins to Strings: A Primer} (\href{https://arxiv.org/abs/1512.07932}{arXiv:1512.07932} ) \item Pan Kessel, \emph{The Very Basics of Higher-Spin Theory} (\href{https://arxiv.org/abs/1702.03694}{arXiv:1702.03694}) \item Ivan Vuković, \emph{Higher spin theory} (\href{https://arxiv.org/abs/1809.02179}{arXiv:1809.02179}) \end{itemize} Further developments include for instance \begin{itemize}% \item Johan Engquist, Olaf Hohm, \emph{Geometry and dynamics of higher-spin frame fields} (\href{http://arxiv.org/abs/0708.1391}{arXiv:0708.1391}) \end{itemize} \hypertarget{ReferencesRelationToStringTheory}{}\subsubsection*{{Relation to string theory}}\label{ReferencesRelationToStringTheory} The idea that higher spin gauge theory appears as the limiting case of [[string field theory]] where the [[string tension]] vanishes goes back to \begin{itemize}% \item [[Marc Henneaux]], [[Claudio Teitelboim]], section 2 of \emph{First And Second Quantized Point Particles Of Any Spin}, in [[Claudio Teitelboim]], [[Jorge Zanelli]] (eds.) \emph{Santiago 1987, Proceedings, Quantum mechanics of fundamental systems 2}, pp. 113-152. Plenum Press. \item [[David Gross]], \emph{High-Energy Symmetries Of String Theory}, Phys. Rev. Lett. 60 (1988) 1229. \end{itemize} and is further developed for instance in \begin{itemize}% \item [[Auguste Sagnotti]], M. Tsulaia, \emph{On higher spins and the tensionless limit of String Theory}, Nucl. Phys. B682:83-116, 2004 (\href{http://arxiv.org/abs/hep-th/0311257}{arXiv:hep-th/0311257}) \item G. Bonelli, \emph{On the Tensionless Limit of Bosonic Strings, Infinite Symmetries and Higher Spins}, Nucl. Phys. B669 (2003) 159-172 (\href{http://arxiv.org/abs/hep-th/0305155}{arXiv:hep-th/0305155}) \item [[Auguste Sagnotti]], M. Taronna, \emph{String Lessons for Higher-Spin Interactions}, Nucl. Phys. B842:299-361,2011 (\href{http://arxiv.org/abs/1006.5242}{arXiv:1006.5242}) \item [[Auguste Sagnotti]], \emph{Notes on Strings and Higher Spins} (\href{http://arxiv.org/abs/1112.4285}{arXiv:1112.4285}) \end{itemize} And conversely: \begin{itemize}% \item Rakibur Rahman, Massimo Taronna, \emph{From Higher Spins to Strings: A Primer} in [[Stefan Fredenhagen]] (ed.) \emph{Introduction to Higher Spin Theory} (\href{https://arxiv.org/abs/1512.07932}{arXiv:1512.07932}) \item [[Matthias Gaberdiel]], [[Rajesh Gopakumar]], \emph{String Theory as a Higher Spin Theory}, J. High Energ. Phys. (2016) 2016: 85 (\href{https://arxiv.org/abs/1512.07237}{arXiv:1512.07237}, ) \item Simon Caron-Huot, Zohar Komargodski, Amit Sever, Alexander Zhiboedov, \emph{Strings from Massive Higher Spins: The Asymptotic Uniqueness of the Veneziano Amplitude}, JHEP10(2017)026 (\href{https://arxiv.org/abs/1607.04253}{arXiv:1607.04253}) \item Amit Sever, Alexander Zhiboedov, \emph{On Fine Structure of Strings: The Universal Correction to the Veneziano Amplitude}, JHEP06(2018)054 (\href{https://arxiv.org/abs/1707.05270}{arXiv:1707.05270}) \end{itemize} \hypertarget{relation_to_other_systems}{}\subsubsection*{{Relation to other systems}}\label{relation_to_other_systems} Relation to [[Kac-Moody algebras]] is discussed in \begin{itemize}% \item [[Marc Henneaux]], [[Axel Kleinschmidt]], [[Hermann Nicolai]], \emph{Higher spin gauge fields and extended Kac-Moody symmetries} (\href{http://arxiv.org/abs/1110.4460}{arXiv:1110.4460}) \end{itemize} Expression in terms of [[AKSZ sigma-models]] is discussed in \begin{itemize}% \item K.B. Alkalaev, Maxim Grigoriev, E.D. Skvortsov, \emph{Uniformizing higher-spin equations} (\href{http://arxiv.org/abs/1409.6507}{arXiv:1409.6507}) \end{itemize} \hypertarget{higher_spin_chernsimons_theory}{}\subsubsection*{{Higher spin Chern-Simons theory}}\label{higher_spin_chernsimons_theory} [[Chern-Simons theory]] for higher spin fields is discussed in \begin{itemize}% \item [[Miles Blencowe]], \emph{A consistent interacting massless higher-spin field theory in $D=2+1$} Classical and quantum gravity, volume 6 no 4 (1998) \item E. S. Fradkin, V. Ya. Linetsky, \emph{a Superconformal Theory of Massless Higher Spin Fields in D=2+1} (\href{http://adsabs.harvard.edu/abs/1989MPLA....4..731F}{web}) \item Johan Engquist, Olaf Hohm, \emph{Higher-spin Chern-Simons theories in odd dimensions} (\href{http://arxiv.org/abs/0705.3714}{arXiv:0705.3714}) \end{itemize} \hypertarget{relation_to_holography}{}\subsubsection*{{Relation to holography}}\label{relation_to_holography} We list references that discuss the relation of higher spin gauge theory to the [[AdS/CFT correspondence]]. \begin{itemize}% \item Simone Giombi, Xi Yin, \emph{Higher Spin Gauge Theory and Holography: The Three-Point Functions} (\href{http://arxiv.org/abs/0912.3462}{arXiv:0912.3462}) \item Simone Giombi, Xi Yin, \emph{Higher Spins in AdS and Twistorial Holography} (\href{http://arxiv.org/abs/1004.3736}{arXiv:1004.3736}) \item Simone Giombi, \emph{TASI Lectures on the Higher Spin - CFT duality} (\href{https://arxiv.org/abs/1607.02967}{arXiv:1607.02967}) \item Charlotte Sleight, \emph{Lectures on Metric-like Methods in Higher Spin Holography} (\href{https://arxiv.org/abs/1701.08360}{arXiv:1701.08360}) \end{itemize} [[!redirects higher spin gauge theories]] [[!redirects higher spin field theory]] [[!redirects higher spin field theories]] [[!redirects higher spin quantum field theory]] [[!redirects higher spin quantum field theories]] \end{document}