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\section*{M-theory}

\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{hints}{Hints}\dotfill \pageref*{hints} \linebreak
\noindent\hyperlink{membranes}{Membranes}\dotfill \pageref*{membranes} \linebreak
\noindent\hyperlink{StronglyCoupledTypeIIAAndD0Branes}{Strongly coupled type IIA strings and D$0$-branes}\dotfill \pageref*{StronglyCoupledTypeIIAAndD0Branes} \linebreak
\noindent\hyperlink{uduality}{U-duality}\dotfill \pageref*{uduality} \linebreak
\noindent\hyperlink{RelationToFTheory}{Relation to F-theory}\dotfill \pageref*{RelationToFTheory} \linebreak
\noindent\hyperlink{cohomological_properties}{Cohomological properties}\dotfill \pageref*{cohomological_properties} \linebreak
\noindent\hyperlink{kaluzaklein_compactifications}{Kaluza-Klein compactifications}\dotfill \pageref*{kaluzaklein_compactifications} \linebreak
\noindent\hyperlink{via_adscft}{Via AdS/CFT}\dotfill \pageref*{via_adscft} \linebreak
\noindent\hyperlink{more}{More}\dotfill \pageref*{more} \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{relation_to_adscft}{Relation to AdS/CFT}\dotfill \pageref*{relation_to_adscft} \linebreak
\noindent\hyperlink{cohomological_considerations}{Cohomological considerations}\dotfill \pageref*{cohomological_considerations} \linebreak
\noindent\hyperlink{relation_to_dbrane_mechanics}{Relation to D$0$-brane mechanics}\dotfill \pageref*{relation_to_dbrane_mechanics} \linebreak
\noindent\hyperlink{more_on_the_relation_to_type_iia_string_theory}{More on the relation to type IIA string theory}\dotfill \pageref*{more_on_the_relation_to_type_iia_string_theory} \linebreak
\noindent\hyperlink{in_terms_of_higher_geometry}{In terms of higher geometry}\dotfill \pageref*{in_terms_of_higher_geometry} \linebreak


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

There are various hints (originally observed in \hyperlink{Witten95}{Witten 95}) that all [[perturbation theory|perturbative]] [[superstring theories]] ([[type II string theory|type II]] (A and B), [[type I string theory|type I]], [[heterotic string theory|heterotic]] ($SO(32)$ and $E_8 \times E_8$)) have a joint [[coupling constant|strong coupling]] [[non-perturbative quantum field theory|non-perturbative]] limit whose low energy [[effective field theory]] description is [[11-dimensional supergravity]] and which reduces to the various string theories by [[Kaluza-Klein compactification]] on an [[orientifold]] torus bundle, followed by various [[duality in string theory|string dualities]]. Since the string itself is thought to arise from a [[membrane]]/[[M2-brane]] in 11-dimensions after [[double dimensional reduction]] this hypothetical theory has been called ``M-theory'' short for ``membrane theory''; e.g. in \hyperlink{HoravaWitten95}{Horava-Witten 95}:

\begin{quote}%
As it has been proposed that the eleven-dimensional theory is a supermembrane theory but there are some reasons to doubt that interpretation, we will non-committally call it the \emph{M-theory}, leaving to the future the relation of M to membranes.


\end{quote}
The ``reasons to doubt'' that interpretation is that the [[M2-brane]] does not support a [[perturbation theory]] the way that the [[superstring]] does. This is part of the reason why the actual nature of ``M-theory'' remains mysterious. On the other hand, later it was argued that there is a regularization of the M2-brane worldvolume theory, which makes it becomes the [[BFSS matrix model]] (\hyperlink{NicolaiHelling98}{Nicolai-Helling 98}, \hyperlink{DasguptaNicolaiPlefka02}{Dasgupta-Nicolai-Plefka 02}). In reaction to these developments it was suggested that ``M-theory'' could be read as ``matrix theory''.

\begin{quote}%
Later, the membranes were interpreted in terms of matrices. Purely by chance, the word ``matrix'' also starts with ``m'', so for a while I would say that the M stands for magic, mystery, or matrix. (\hyperlink{Witten14}{Witten 14, last paragraph})


\end{quote}
The defining characteristic of M-theory is that it exhibits [[duality between M-theory and type IIA string theory|duality with type IIA string theory]] in the following way:

\begin{displaymath}
\itexarray{
      M-Theory(?) &\stackrel{low\;energy\;limit}{\to}& 11d Supergravity
      \\
      {}^{\mathllap{ \itexarray{ small \\ coupling \\ limit}}}\downarrow && \downarrow^{\mathrlap{ \itexarray{KK\;reduction \\ on S^1 }}}
      \\
      type IIA string theory 
        &\stackrel{low\;energy\;effective\;QFT}{\to}&  
      10d Supergravity
  }
\end{displaymath}
(see also e.g. (\hyperlink{ObersPioline98}{Obers-Pioline 98, p. 12})). The unknown top left corner here has optimistically been given a name, and that is ``M-theory''. But even the rough global structure of the top left corner has remained elusive.

\begin{quote}%
We still have no fundamental formulation of ``[[M-theory]]'' - the hypothetical theory of which [[11-dimensional supergravity]] and the five [[string theories]] are all special limiting cases. Work on formulating the fundamental principles underlying M-theory has noticeably waned. $[...]$. If history is a good guide, then we should expect that anything as profound and far-reaching as a fully satisfactory formulation of M-theory is surely going to lead to new and novel mathematics. Regrettably, it is a problem the community seems to have put aside - temporarily. But, ultimately, Physical Mathematics must return to this grand issue.

(\href{Physical+Mathematics+and+the+Future#Moore14}{Moore 14, section 12})


\end{quote}
\hypertarget{hints}{}\subsection*{{Hints}}\label{hints}

The available evidence that there is something of interest consists of various facets of the bottom left and the top right entry of the above diagram, that seem to have a common origin in the top left corner.

\hypertarget{membranes}{}\subsubsection*{{Membranes}}\label{membranes}

Notably, from the [[black brane]]-solution structure in [[11-dimensional supergravity]] and from the [[brane scan]] one finds that it contains a 2-[[brane]], called the \emph{[[M2-brane]]}, and to the extent that one has this under control one can show that under ``double dimensional reduction'' this becomes the [[string]]. However, it is clear that this cannot quite give a definition of the top left corner by [[perturbation theory]] as the [[superstring]] [[sigma-model]] does for the bottom left corner. At the bottom of it, this is simply because, by the very nature of the conjecture, the top left corner is supposed to be given by a non-perturbative strong-coupling limit of the bottom left corner. But one may also see that the evident guess for a would-be membrane analog of the [[string perturbation series]] fails

\begin{quote}%
 [[Mike Duff]], [[Paul Townsend]], and other physicists working on [[supermembranes]] had spent a couple of years in the mid-1980s saying that there should be a theory of fundamental membranes analogous to the theory of fundamental strings. That wasn't convincing for a large number of reasons. For one thing, a three-manifold doesn't have an [[Euler characteristic]], so there isn't a topological expansion as there is in string theory. Moreover, in three dimensions there is no [[conformal invariance]] to help us make sense of membrane theory; membrane theory is [[renormalization|nonrenormalizable]] just like [[general relativity]].

([[Edward Witten]] in interview by [[Hirosi Ooguri]], Notices Amer. Math. Soc, May 2015 p491 (\href{http://www.ams.org/notices/201505/rnoti-p491.pdf}{pdf}))


\end{quote}
This issue is the very root of the abbreviation ``M-theory'':

\begin{quote}%
As it has been proposed that the eleven-dimensional theory is a supermembrane theory but there are some reasons to doubt that interpretation, we will non-committally call it the \emph{M-theory}, leaving to the future the relation of M to membranes. (\hyperlink{HoravaWitten95}{Horava-Witten 95})

 M-theory was meant as a temporary name pending a better understanding. Some colleagues thought that the theory should be understood as a membrane theory. Though I was skeptical, I decided to keep the letter ``m'' from ``membrane'' and call the theory M--theory, with time to tell whether the M stands for magic, mystery, or membrane. Later, the membranes were interpreted in terms of matrices. Purely by chance, the word ``matrix'' also starts with ``m'', so for a while I would say that the M stands for magic, mystery, or matrix. (\hyperlink{Witten14}{Witten 14, last paragraph})


\end{quote}
\hypertarget{StronglyCoupledTypeIIAAndD0Branes}{}\subsubsection*{{Strongly coupled type IIA strings and D$0$-branes}}\label{StronglyCoupledTypeIIAAndD0Branes}

There is a bunch of consistency checks on the statement that the [[KK-compactification]] of [[11-dimensional supergravity]] on a circle gives the [[non-perturbative quantum field theory|strong coupling]] refinement of [[type IIA string theory]]. See at \emph{[[duality between M-theory and type IIA string theory]]}.

One aspect of this is that [[type IIA string theory]] with a [[condensate]] of [[D0-branes]] behaves like a 10-dimensional theory that develops a further circular dimension of [[radius]] scaling with the density of [[D0-branes]]. (\hyperlink{BanksFischlerShenkerSusskind97}{Banks-Fischler-Shenker-Susskind 97}, \hyperlink{Polchinski99}{Polchinski 99}). See also (\hyperlink{FSS13}{FSS 13, section 4.2}).

Discussion of the relation of [[gauge enhancement]] of M-theory at [[ADE singularities]] and the corresponding coincident [[D-brane]] geometries in type IIA string theory is in (\hyperlink{Sen97}{Sen 97}).

More on the decomposition of the [[nLab:supergravity C-field]] in 11d to the [[RR-fields]] and the NS-fields in type IIA is in (\hyperlink{MathaiSati03}{Mathai-Sati 03, section 4}).

For survey of how the components maps see also the table at \emph{\hyperlink{RelationToFTheory}{Relation to F-theory}}.

\hypertarget{uduality}{}\subsubsection*{{U-duality}}\label{uduality}

Another hint comes from the fact that the [[U-duality]]-structure of [[supergravity]] theories forms a clear pattern in those dimensions where one understands it well, giving rise to a description of higher dimensional supergravity theories by [[exceptional generalized geometry]]. Now, this pattern, as a mathematical pattern, can be continued to the case that would correspond to the top left corner above, by passing to [[exceptional generalized geometry]] over \emph{hyperbolic} [[Kac-Moody Lie algebras]] such as first [[E10]] and then, ultimately [[E11]]. The references there show that these are huge algebraic structures inside which people incrementally find all kinds of relations that are naturally identified with various aspects of M-theory. This leads to the conjecture that M-theory somehow \emph{is} $E_{11}$ in some way. But it all remains rather mysterious at the moment.

\hypertarget{RelationToFTheory}{}\subsubsection*{{Relation to F-theory}}\label{RelationToFTheory}

The [[KK-compactification|compactification]] of M-theory on a torus yields [[type II string theory]] -- directly type IIA, and then type IIB after [[T-duality|T-dualizing]]. It turns out that the [[axio-dilaton]] of the resulting type II-B string theory is equivalently the [[complex structure]]-[[moduli|modulus]] of this [[elliptic fibration]] by the compactification torus. This gives a description of [[non-perturbative quantum field theory|non-perturbative]] aspects of type II which has come to be known as \emph{[[F-theory]]} (see e.g. \hyperlink{Johnson97}{Johnson 97}).

In slightly more detail, write, topologically, $T^2 = S^1_A\times S^1_B$ for the compactification torus of M-theory, where contracting the first $S^1_A$-factor means passing to type IIA. To obtain type IIB in noncompact 10 dimensions from M-theory, also the second $S^1_B$ is to be compactified (since [[T-duality]] sends the radius $r_A$ of $S^1_A$ to the inverse radius $r_B = \ell_s^2 / R_A$ of $S^1_B$). Therefore type IIB sugra in $d = 10$ is obtained from 11d sugra compactified on the [[torus]] $S^1_A \times S^1_B$. More generally, this torus may be taken to be an [[elliptic curve]] and this may vary over the 9d base space as an [[elliptic fibration]].

Applying T-duality to one of the compact direction yields a 10-dimensional theory which may now be thought of as encoded by a 12-dimensional elliptic fibration. This 12d elliptic fibration encoding a 10d type II supergravity [[vacuum]] is the input data that [[F-theory]] is concerned with.

A schematic depiction of this story is the following:

\newline In the simple case where the elliptic fiber is indeed just $S^1_A \times S^1_B$, the [[imaginary part]] of its complex modulus is

\begin{displaymath}
Im(\tau) = \frac{R_A}{R_B}
  \,.
\end{displaymath}
By following through the above diagram, one finds how this determines the [[coupling constant]] in the [[type II string theory]]:

First, the [[KK-compactification]] of M-theory on $S^1_A$ yields a type IIA [[string coupling constant]]

\begin{displaymath}
g_{IIA} = \frac{R_A}{\ell_s}
  \,.
\end{displaymath}
Then the T-duality operation along $S^1_B$ divides this by $R_B$:

\begin{displaymath}
\begin{aligned}
    g_{IIB} & = g_{IIA} \frac{\ell_s}{R_B} 
    \\
    & = \frac{R_A}{R_B}
    \\
    & = Im(\tau)
   \end{aligned}
   \,.
\end{displaymath}
[[!include F-branes -- table]]

\hypertarget{cohomological_properties}{}\subsubsection*{{Cohomological properties}}\label{cohomological_properties}

A derivation of [[D-brane charge]], [[RR-fields]] and other [[K-theory]] structure in [[type II superstring theory]] from M-theory was argued in (\hyperlink{FMW00}{FMW 00}).

See also at \emph{[[cubical structure in M-theory]]}.

\hypertarget{kaluzaklein_compactifications}{}\subsubsection*{{Kaluza-Klein compactifications}}\label{kaluzaklein_compactifications}

[[!include KK-compactifications of M-theory -- table]]

\hypertarget{via_adscft}{}\subsubsection*{{Via AdS/CFT}}\label{via_adscft}

The [[AdS-CFT duality]] for the [[black brane|black]][[M5-brane]] may be turned around to deduce from the [[6d (2,0)-superconformal QFT]] on the [[M5-brane]] [[scattering amplitudes]] in the 11-dimensional [[bulk]]-spacetime, hence in putative M-theory. While the [[6d (2,0)-superconformal QFT]] is not completely known, [[conformal invariance]] and [[supersymmetry]] tightly constrains it (``[[conformal bootstrap]]'') and does allow to extract results.

This approach to computing putative M-theory scattering amplitudes is due to (\hyperlink{ChesterPerlmutter18}{ChesterPerlmutter18}).

\hypertarget{more}{}\subsubsection*{{More}}\label{more}

(\ldots{})

\hypertarget{related_entries}{}\subsection*{{Related entries}}\label{related_entries}

\begin{itemize}%
\item [[F-theory]]


\item [[topological M-theory]], [[bosonic M-theory]]


\item [[M2-brane]], [[M5-brane]]


\item [[supergravity Lie 3-algebra]], [[supergravity Lie 6-algebra]], [[M-theory super Lie algebra]]


\item [[Horava-Witten theory]], [[M9-brane]]


\item [[M-theory on G2-manifolds]]

\begin{itemize}%
\item [[G2-MSSM]]

\end{itemize}

\item [[M-theory on 8-manifolds]]


\item [[Diaconescu-Moore-Witten anomaly]]


\item [[BFSS matrix model]], [[IKKT matrix model]], [[membrane matrix model]]



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

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

First indications for M-theory came from the [[supermembrane]] [[Green-Schwarz sigma-model]] now called the [[M2-brane]]. A comprehensive collection of early articles is in

\begin{itemize}%
\item [[Mike Duff]], \emph{[[The World in Eleven Dimensions]]: Supergravity, Supermembranes and M-theory}, IoP 1999 (\href{https://www.crcpress.com/The-World-in-Eleven-Dimensions-Supergravity-supermembranes-and-M-theory/Duff/9780750306720}{publisher})

\end{itemize}
For some time though the success of [[string theory]] in 10-dimensions caused resistence to the idea of a theory of [[membranes]] in 11-dimensions, an account is in (\hyperlink{Duff99}{Duff 99}) and in brevity on the first pages of

\begin{itemize}%
\item [[Mike Duff]], \emph{M-history without the M} (\href{http://arxiv.org/abs/1501.04098}{arXiv:1501.04098})

\end{itemize}
The article that convinced the community of M-theory was

\begin{itemize}%
\item [[Edward Witten]], \emph{[[String Theory Dynamics In Various Dimensions]]}, Nucl.Phys.B443:85-126 (1995) (\href{http://arxiv.org/abs/hep-th/9503124}{arXiv:hep-th/9503124})

\end{itemize}
A public talk announcing the conjecture that the [[non-perturbative field theory|strong-coupling limit]] of [[type IIA string theory]] is [[11-dimensional supergravity]] [[KK-compactification|KK-compactified]] on a circle is at 15:12 in

\begin{itemize}%
\item [[Edward Witten]], \href{https://youtu.be/1HYa4wxqe8Y}{video})19:33: ``Ten years ago we had the embarrassment that there were five consistent string theories plus a close cousin, which was 11-dimensional supergravity.'' (19:40): ``I promise you that by the end of the talk we have just one big theory.''



\end{itemize}
The term ``M-theory'' originates in

\begin{itemize}%
\item [[Petr Hořava]], [[Edward Witten]], \emph{Heterotic and Type I string dynamics from eleven dimensions}, Nucl. Phys. B460 (1996) 506 (\href{http://arxiv.org/abs/hep-th/9510209}{arXiv:hep-th/9510209})

\end{itemize}
as a ``non-committed'' shorthand for ``membrane theory''

\begin{quote}%
 As it has been proposed that the eleven-dimensional theory is a supermembrane theory but there are some reasons to doubt that interpretation, we will non-committally call it the M-theory, leaving to the future the relation of M to membranes. (\hyperlink{HoravaWitten95}{Hoava-Witten 95, p. 2})


\end{quote}
and

\begin{itemize}%
\item [[Edward Witten]], \emph{Five-branes And M-Theory On An Orbifold}, Nucl.Phys.B463:383-397,1996 (\href{http://arxiv.org/abs/hep-th/9512219}{arXiv:hep-th/9512219})

\end{itemize}
which coined the association

\begin{quote}%
the eleven-dimensional ``M-theory'' (where M stands for magic, mystery, or membrane, according to taste) (\hyperlink{Witten95}{Witten 95, p. 1})


\end{quote}
that later gained much publicity:

\begin{itemize}%
\item [[Edward Witten]], \emph{Magic, Mystery, and Matrix}, Notices of the AMS, volume 45, number 9 (1998) (\href{http://www.ams.org/notices/199809/witten.pdf}{pdf})

\end{itemize}
The argument that the regularized [[M2-brane]] [[worldvolume]] theory is the [[BFSS matrix model]] is discussed in

\begin{itemize}%
\item [[Hermann Nicolai]], Robert Helling, \emph{Supermembranes and M(atrix) Theory}, Lectures given by H. Nicolai at the Trieste Spring School on Non-Perturbative Aspects of String Theory and Supersymmetric Gauge Theories, 23 - 31 March 1998 (\href{http://arxiv.org/abs/hep-th/9809103}{arXiv:hep-th/9809103})


\item Arundhati Dasgupta, [[Hermann Nicolai]], [[Jan Plefka]], \emph{An Introduction to the Quantum Supermembrane}, Grav.Cosmol.8:1,2002; Rev.Mex.Fis.49S1:1-10, 2003 (\href{http://arxiv.org/abs/hep-th/0201182}{arXiv:hep-th/0201182})



\end{itemize}
Recollections include the last paragraph of

\begin{itemize}%
\item [[Edward Witten]], \emph{Adventures in Physics and Math}, \href{http://www.kyotoprize.org/en/laureates/commemorative_lectures/}{Kyoto Prize lecture} 2014 (\href{http://www.kyotoprize.org/wp/wp-content/uploads/2016/02/30kB_lct_EN.pdf}{pdf}, [[WittenKyotoPrizeLecture.pdf:file]])

\end{itemize}
The term became fully established with surveys including

\begin{itemize}%
\item [[Michael Duff]], \emph{M-Theory (the Theory Formerly Known as Strings)}, Int. J. Mod. Phys. A11 (1996) 5623-5642 (\href{http://arxiv.org/abs/hep-th/9608117}{arXiv:hep-th/9608117})


\item [[Michael Duff]], \emph{The Theory Formerly Known as Strings}, Scientific American 1998 (\href{https://www.nikhef.nl/pub/services/biblio/bib_KR/sciam14395569.pdf}{pdf})


\item [[Michael Duff]], \emph{A Layman's Guide to M-theory} (\href{https://arxiv.org/abs/hep-th/9805177}{arXiv:hep-th/9805177})



\end{itemize}
Despite the magic and mystery, the relation to the original abbreviation for \emph{membrane-theory} was highlighted again for instance in

\begin{itemize}%
\item [[Paul Townsend]], \emph{M(embrane) theory on $T^0$}, Nucl.Phys.Proc.Suppl.68:11-16,1998 (\href{http://arxiv.org/abs/hep-th/9708034}{arXiv:hep-th/9708034})

\end{itemize}
More recent review includes

\begin{itemize}%
\item N.A. Obers, B. Pioline, \emph{U-duality and M-Theory}, Phys.Rept.318:113-225,1999 (\href{http://arxiv.org/abs/hep-th/9809039}{arXiv:hep-th/9809039})

\end{itemize}
Early articles clarifying the relation to [[type II string theory]] now known as [[F-theory]] include

\begin{itemize}%
\item [[John Schwarz]], \emph{The Power of M Theory}, Phys.Lett. B367 (1996) 97-103 (\href{http://arxiv.org/abs/hep-th/9510086}{arXiv:hep-th/9510086})


\item [[Clifford Johnson]], \emph{From M-theory to F-theory, with Branes}, Nucl.Phys. B507 (1997) 227-244 (\href{http://arxiv.org/abs/hep-th/9706155}{arXiv:hep-th/9706155})



\end{itemize}
The relation also to the [[heterotic string]] was understood in (\hyperlink{HoravaWitten95}{Horava-Witten 95}) see at \emph{[[Horava-Witten theory]]}.

More technical surveys include

\begin{itemize}%
\item [[Paul Townsend]], \emph{Four Lectures on M-theory}, procs. of the ICTP summer school on High Energy Physics and Cosmology, Trieste, June 1996. (\href{http://arxiv.org/abs/hep-th/9612121}{arXiv:hep-th/9612121})

\end{itemize}
Surveys of the discussion of E-series [[Kac-Moody algebras]]/[[Kac-Moody groups]] in the context of M-theory include

\begin{itemize}%
\item Sophie de Buyl, \emph{Kac-Moody Algebras in M-theory}, PhD thesis (\href{http://theses.ulb.ac.be/ETD-db/collection/available/ULBetd-06072006-153117/unrestricted/kmalgebrasinmth.pdf}{pdf})


\item [[Paul Cook]], \emph{Connections between Kac-Moody algebras and M-theory} PhD thesis (\href{http://arxiv.org/abs/0711.3498}{arXiv:0711.3498})



\end{itemize}
\hypertarget{relation_to_adscft}{}\subsubsection*{{Relation to AdS/CFT}}\label{relation_to_adscft}

Relation to [[AdS/CFT]] and [[conformal bootstrap]]:

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

\end{itemize}
\hypertarget{cohomological_considerations}{}\subsubsection*{{Cohomological considerations}}\label{cohomological_considerations}

Discussion of the [[cohomology|cohomological]] charge quantization in type II ([[RR-fields]] as cocycles in [[KR-theory]]) in relation to the M-theory [[supergravity C-field]] is in

\begin{itemize}%
\item D. Diaconescu, [[Gregory Moore]], [[Edward Witten]], \emph{$E_8$ Gauge Theory, and a Derivation of K-Theory from M-Theory}, Adv.Theor.Math.Phys.6:1031-1134,2003 (\href{http://arxiv.org/abs/hep-th/0005090}{arXiv:hep-th/0005090}), summarised in \emph{A Derivation of K-Theory from M-Theory} (\href{http://arxiv.org/abs/hep-th/0005091}{arXiv:hep-th/0005091})

\end{itemize}
See also

\begin{itemize}%
\item Inaki Garcia-Etxebarria, [[Angel Uranga]], \emph{From F/M-theory to K-theory and back}, JHEP 0602:008,2006 (\href{https://arxiv.org/abs/hep-th/0510073}{arXiv:hep-th/0510073})

\end{itemize}
For more on this perspective as 10d type II as a [[self-dual higher gauge theory]] in the boudnary of a kind of [[higher dimensional Chern-Simons theory|11-d Chern-Simons theory]] is in

\begin{itemize}%
\item Dmitriy Belov, [[Greg Moore]], \emph{Type II Actions from 11-Dimensional Chern-Simons Theories} (\href{http://arxiv.org/abs/hep-th/0611020}{arXiv:hep-th/0611020})

\end{itemize}
More complete discussion of the decomposition of the [[supergravity C-field]] as one passes from 11d to 10d is in

\begin{itemize}%
\item [[Varghese Mathai]], [[Hisham Sati]], \emph{Some Relations between Twisted K-theory and E8 Gauge Theory}, JHEP0403:016,2004 (\href{http://arxiv.org/abs/hep-th/0312033}{arXiv:hep-th/0312033})

\end{itemize}
\hypertarget{relation_to_dbrane_mechanics}{}\subsubsection*{{Relation to D$0$-brane mechanics}}\label{relation_to_dbrane_mechanics}

Discussion of M-theory as arising from [[type II string theory]] via the effect of [[D0-branes]] is in

\begin{itemize}%
\item [[Tom Banks]], W. Fischler, S.H. Shenker, [[Leonard Susskind]], \emph{M Theory As A Matrix Model: A Conjecture}, Phys.Rev.D55:5112-5128,1997 (\href{http://arxiv.org/abs/hep-th/9610043}{arXiv:hep-th/9610043})

\end{itemize}
\begin{itemize}%
\item [[Joseph Polchinski]], \emph{M-Theory and the Light Cone}, Prog.Theor.Phys.Suppl.134:158-170,1999 (\href{http://arxiv.org/abs/hep-th/9903165}{arXiv:hep-th/9903165})

\end{itemize}
\hypertarget{more_on_the_relation_to_type_iia_string_theory}{}\subsubsection*{{More on the relation to type IIA string theory}}\label{more_on_the_relation_to_type_iia_string_theory}

\begin{itemize}%
\item [[Ashoke Sen]], \emph{A Note on Enhanced Gauge Symmetries in M- and String Theory}, JHEP 9709:001,1997 (\href{http://arxiv.org/abs/hep-th/9707123}{arXiv:hep-th/9707123})

\end{itemize}
\hypertarget{in_terms_of_higher_geometry}{}\subsubsection*{{In terms of higher geometry}}\label{in_terms_of_higher_geometry}

Discussion of phenomena of M-theory in [[higher geometry]] and [[generalized cohomology]] is in

\begin{itemize}%
\item [[Hisham Sati]], \emph{[[Geometric and topological structures related to M-branes]]} (2010)

\end{itemize}
See also the references at \emph{[[exceptional generalized geometry]]}.

In fact, much of the broad structure of M-theory and its relation to the various [[string theory]] limits can be seen from the classification of exceptional [[super L-∞ algebras]] (such as the [[supergravity Lie 3-algebra]] and the [[supergravity Lie 6-algebra]]), as discussed in

\begin{itemize}%
\item [[Domenico Fiorenza]], [[Hisham Sati]], [[Urs Schreiber]], \emph{[[schreiber:The brane bouquet|Super Lie n-algebra extensions, higher WZW models and super p-branes with tensor multiplet fields]]} (\href{http://arxiv.org/abs/1308.5264}{arXiv:1308.5264})

\end{itemize}
By passing to [[automorphism]] algebras, this reproduces the polyvector extensions of the [[super Poincaré Lie algebra]], which enter the traditional discussion of M-theory, such as the [[M-theory super Lie algebra]] (which arises as the symmetries of the [[M5-brane]] [[schreiber:∞-Wess-Zumino-Witten theory]]).

[[!redirects non-perturbative string theory]]



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