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\begin{document}

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\section*{spinning string}

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

\hypertarget{string_theory}{}\paragraph*{{String theory}}\label{string_theory}

[[!include string theory - contents]]

\hypertarget{quantum_field_theory}{}\paragraph*{{Quantum field theory}}\label{quantum_field_theory}

[[!include functorial quantum field theory - contents]]

\hypertarget{physics}{}\paragraph*{{Physics}}\label{physics}

[[!include physicscontents]]

\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{gso_projection_and_spacetime_supersymmetry}{GSO projection and spacetime supersymmetry}\dotfill \pageref*{gso_projection_and_spacetime_supersymmetry} \linebreak
\noindent\hyperlink{brst_description}{BRST description}\dotfill \pageref*{brst_description} \linebreak


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

The \emph{spinning string} is a variant of the [[string]] in direct analogy (but one [[worldvolume]] [[dimension]] higher) to how the [[spinning particle]] is a variant of the [[particle]].

(Which means that ``spinning'' here is \emph{not} in the sense of ``rotating'', but in the sense of the kind of ``intrinsic'' spin as exhibited by [[fermion]] [[particle]]s. A spinning string can rotate \emph{in addition} to its intrinsic spin.)

And just as as the [[spinning particle]] automatically exhibits local [[worldline supersymmetry]], the spinning string automatically exhibits local [[worldsheet]] [[supersymmetry]]. For that reason it is today almost exclusively known as the \emph{[[superstring]]} .

In fact, the very notion of [[supersymmetry]] was realized (in parallel to its independent discovery in Russia) when people noticed that the spinning string [[sigma-model]] -- also called the \emph{Neveu-Ramond-Schwarz model} (\textbf{NSR model}) -- automatically exhibits this extra graded symmetry.

When supplemented with an operation called the \emph{[[GSO projection]]}, the [[second quantization]] of the spinning string -- its effective [[target space|target]] [[spacetime]] theory -- also becomes a locally supersymmetric theory: [[spacetime]] [[supergravity]].

There are other formulations of the [[superstring]] which are thought to be equivalent in some sense. Notably the [[Green-Schwarz superstring]] is a sigma-model which is not supersymmetric on the [[worldsheet]] but instead takes values in a genuine [[spacetime]] [[supermanifold]].

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

\begin{itemize}%
\item [[picture number]], [[picture changing operator]]


\item [[sigma model]], [[brane]]

\begin{itemize}%
\item [[relativistic particle]], [[spinning particle]], [[superparticle]]


\item [[string]], \textbf{spinning string} , [[superstring]]


\item [[Goddard-Thorn no-ghost theorem]], [[GSO projection]]

\href{string+theory+FAQ#DoesSTPredictSupersymmetry}{string theory FAQ -- Does string theory predict supersymmetry?}


\item [[membrane]]



\end{itemize}

\item [[string theory]]



\end{itemize}
[[!include worldvolume-target supersymmetry of brane sigma-models]]

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

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

The original articles that formulated the NSR model are

\begin{itemize}%
\item [[André Neveu]], [[John Schwarz]], \emph{Factorizable dual model of pions}, Nucl. Phys. B31, 86 (1971) ()


\item [[Pierre Ramond]], \emph{Dual theory for Free Fermions}, Phys Rev. D3 2415 (1971) (\href{https://doi.org/10.1103/PhysRevD.3.2415}{doi:10.1103/PhysRevD.3.2415})


\item [[Daniel Friedan]], [[Emil Martinec]], [[Stephen Shenker]], \emph{Conformal invariance, supersymmetry and string theory}, Nucl. Phys., B271 (1986) 93 ()



\end{itemize}
Original articles that realize the local [[worldsheet]] [[supersymmetry]] of the spinning string include

\begin{itemize}%
\item [[Stanley Deser]], [[Bruno Zumino]], \emph{A complete action for the spinning string} Physics Letters B 65 (4): 369-373 (1976) (\href{http://cdsweb.cern.ch/record/201648/files/CM-P00061857.pdf?version=1}{pdf})


\item L. Brink, P. Di Vecchia and [[Paul Howe]], \emph{A locally supersymmetric and reparametrization invariant action for the spinning string} , Physics Letters B Volume 65, Issue 5, 20 (1976) Pages 471-474



\end{itemize}
Definition of the NSR string in [[RR-field]] [[background field|backgrounds]] is subtle (in contrast to the classical [[Green-Schwarz superstring]]), discussion is in

\begin{itemize}%
\item [[David Berenstein]], Robert Leigh, \emph{Superstring Perturbation Theory and Ramond-Ramond Backgrounds}, Phys. Rev. D 60, 106002 (1999) (\href{https://arxiv.org/abs/hep-th/9904104}{arXiv:hep-th/9904104})

\end{itemize}
\hypertarget{gso_projection_and_spacetime_supersymmetry}{}\subsubsection*{{GSO projection and spacetime supersymmetry}}\label{gso_projection_and_spacetime_supersymmetry}

The [[GSO projection]] and the conjecture that this makes also the target space theory of the spinning string [[supergravity|locally supersymmetric]] is due to

\begin{itemize}%
\item F. Gliozzi, [[Joël Scherk]], D. I. Olive, \emph{Supergravity and its spinor dual model,} Phys. Letters B65, 282 (1976)


\item F. Gliozzi, [[Joël Scherk]], D. I. Olive, \emph{Supersymmetry, supergravity theories and the dual spinor model} , Nucl. Phys, B122, 253 (1977)



\end{itemize}
The demonstration of this fact is due to

\begin{itemize}%
\item [[Michael Green]], [[John Schwarz]],

\emph{Supersymmetrical dual string theory} , Nucl. Phys. B181 (1981) 502;

\emph{Supersymmetrical string theories} , Phys. Lett. 109B (1982) 444.



\end{itemize}
Superconformal invariance of the spinning string was discussed in

\begin{itemize}%
\item [[Paul Howe]], \emph{Super Weyl transformations in two dimensions} J. Phys. 12 (1979) 393.

\end{itemize}
A decent account is in

\begin{itemize}%
\item Imre Majer, \emph{Superstrings} (\href{http://edu.itp.phys.ethz.ch/fs13/cft/SuperS2_Majer.pdf}{pdf}, [[MajerSuperstrings.pdf:file]])

\end{itemize}
A review of the history of these developments is in

\begin{itemize}%
\item [[John Schwarz]], \emph{String theory origins of supersymmetry}, Nucl. Phys. Proc. Suppl. 101 (2001) 54-61 (\href{http://arxiv.org/abs/hep-th/0011078}{arXiv:hep-th/0011078})

\end{itemize}
An exposition of some technical aspects is in the wiki

\begin{itemize}%
\item \href{http://www.physics.thetangentbundle.net/wiki/Main_Page}{The Tangent Bundle}, \emph{\href{http://www.physics.thetangentbundle.net/wiki/String_theory/RNS_superstring}{RNS superstring}}

\end{itemize}
Reviews and survays are also in any text on [[string theory]]. See the references there for more detail.

\hypertarget{brst_description}{}\subsubsection*{{BRST description}}\label{brst_description}

Discussion of the [[BRST complex]] of the NSR string is for instance in

\begin{itemize}%
\item [[José Figueroa-O'Farrill]], Takashi Kimura, \emph{The BRST cohomology of the NSR string: vanishing and ``no-ghost'' theorems} (\href{http://www.maths.ed.ac.uk/~jmf/Research/PVBLICATIONS/nsr.pdf}{pdf})

\end{itemize}
[[!redirects spinning strings]]

[[!redirects NSR string]] [[!redirects NSR strings]]

[[!redirects NSR superstring]] [[!redirects NSR superstrings]]

[[!redirects NSR-string]] [[!redirects NSR-strings]]

[[!redirects NSR-superstring]] [[!redirects NSR-superstrings]]

[[!redirects RNS string]] [[!redirects RNS strings]]

[[!redirects RNS superstring]] [[!redirects RNS superstrings]]

[[!redirects RNS-string]] [[!redirects RNS-strings]]

[[!redirects RNS-superstring]] [[!redirects RNS-superstrings]]

[[!redirects Neveu-Ramond-Schwarz model]] [[!redirects Neveu-Ramond-Schwarz models]]

[[!redirects Neveu-Ramond-Schwarz string]] [[!redirects Neveu-Ramond-Schwarz strings]]

[[!redirects Neveu-Ramond-Schwarz superstring]] [[!redirects Neveu-Ramond-Schwarz superstrings]]

[[!redirects Neveu-Ramond-Schwarz super-string]] [[!redirects Neveu-Ramond-Schwarz super-strings]]

[[!redirects Ramond-Neveu-Schwarz string]] [[!redirects Ramond-Neveu-Schwarz strings]]

[[!redirects Ramond-Neveu-Schwarz model]] [[!redirects Ramond-Neveu-Schwarz models]]

[[!redirects Neveu-Schwarz-Ramond superstring]] [[!redirects Neveu-Schwarz-Ramond superstrings]]

[[!redirects Neveu-Schwarz-Ramond super-string]] [[!redirects Neveu-Schwarz-Ramond super-strings]]

[[!redirects Neveu-Schwarz-Ramond string]] [[!redirects Neveu-Schwarz-Ramond strings]]

[[!redirects Neveu-Schwarz-Ramond model]] [[!redirects Neveu-Schwarz-Ramond models]]



\end{document}