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\begin{document}

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\section*{D=11 N=1 supergravity}

[[!redirects 11-dimensional supergravity]] [[!redirects 11-dimensional supergravity]]

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

\hypertarget{gravity}{}\paragraph*{{Gravity}}\label{gravity}

[[!include gravity contents]]

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

[[!include string 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{the_action_functional}{The action functional}\dotfill \pageref*{the_action_functional} \linebreak
\noindent\hyperlink{kinetic_terms}{Kinetic terms}\dotfill \pageref*{kinetic_terms} \linebreak
\noindent\hyperlink{the_higher_chernsimons_term}{The higher Chern-Simons term}\dotfill \pageref*{the_higher_chernsimons_term} \linebreak
\noindent\hyperlink{HigherCurvatureCorrection}{Higher curvature corrections}\dotfill \pageref*{HigherCurvatureCorrection} \linebreak
\noindent\hyperlink{the_hidden_deformation}{The hidden deformation}\dotfill \pageref*{the_hidden_deformation} \linebreak
\noindent\hyperlink{bps_states}{BPS states}\dotfill \pageref*{bps_states} \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{classical_solutions_and_bps_states}{Classical solutions and BPS states}\dotfill \pageref*{classical_solutions_and_bps_states} \linebreak
\noindent\hyperlink{ReferencesHigherCurvatureCorrections}{Higher curvature corrections}\dotfill \pageref*{ReferencesHigherCurvatureCorrections} \linebreak
\noindent\hyperlink{scattering_amplitudes_and_effective_action}{Scattering amplitudes and Effective action}\dotfill \pageref*{scattering_amplitudes_and_effective_action} \linebreak
\noindent\hyperlink{truncations_and_compactifications}{Truncations and compactifications}\dotfill \pageref*{truncations_and_compactifications} \linebreak
\noindent\hyperlink{topology_and_anomaly_cancellation}{Topology and anomaly cancellation}\dotfill \pageref*{topology_and_anomaly_cancellation} \linebreak
\noindent\hyperlink{description_by_exceptional_generalized_geometry}{Description by exceptional generalized geometry}\dotfill \pageref*{description_by_exceptional_generalized_geometry} \linebreak


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

$N=1$ [[supergravity]] in $d = 11$.

\begin{quote}%
for the moment see the respective section at [[D'Auria-Fre formulation of supergravity]]


\end{quote}
\hypertarget{the_action_functional}{}\subsection*{{The action functional}}\label{the_action_functional}

(\ldots{})

\hypertarget{kinetic_terms}{}\subsubsection*{{Kinetic terms}}\label{kinetic_terms}

(\ldots{})

\hypertarget{the_higher_chernsimons_term}{}\subsubsection*{{The higher Chern-Simons term}}\label{the_higher_chernsimons_term}

\begin{quote}%
under construction


\end{quote}
\begin{displaymath}
\int_X
  \left(
  \frac{1}{6} 
  \left(
    C \wedge G \wedge G
    -
    C \wedge
    \frac{1}{8}
    \left(
      p_2 + (\frac{1}{2}p_1)^2 
    \right)
  \right)
  \right)
\end{displaymath}
where $p_i$ is the $i$th [[Pontryagin class]].

\begin{displaymath}
\lambda := \frac{1}{2}p_1
  \,.
\end{displaymath}
Concerning the integrality of

\begin{displaymath}
I_8 := \frac{1}{48}(p_2 + (\lambda)^2)
\end{displaymath}
on a [[spin structure|spin manifold]] $X$. (\hyperlink{Witten96}{Witten96, p.9})

First, the [[index]] of a [[Dirac operator]] on $X$ is

\begin{displaymath}
I = \frac{1}{1440}(7 (\frac{1}{2}p_1)^2 - p_2) \in \mathbb{Z}
  \,.
\end{displaymath}
Notice that $1440 = 6 \times 8 \times 30$. So

\begin{displaymath}
p_2 - (\frac{1}{2}p_2)^2 = 6 ( (\frac{1}{2}p_1)^2 - 30 \times 8 I)
\end{displaymath}
is divisible by 6.

Assume that $(\frac{1}{2}p_1)$ is further divisible by 2 (see the relevant discussion at \emph{[[M5-brane]]}).

\begin{displaymath}
(\frac{1}{2}p_1) = 2 x
  \,.
\end{displaymath}
Then the above becomes

\begin{displaymath}
p_2 - (\frac{1}{2}p_2)^2 = 24 ( x^2 - 30 \times 2 I)
\end{displaymath}
and hence then $p_2 + (\frac{1}{2}p_1)^2$ is divisible at least by 24.

But moreover, on a [[spin structure|Spin manifold]] the [[first fractional Pontryagin class]] $\frac{1}{2}p_1$ is the [[Wu class]] $\nu_4$ (see there). By definition this means that

\begin{displaymath}
x^2 = x (\frac{1}{2}p_1) \; mod \; 2
\end{displaymath}
and so when $(\frac{1}{2}p_1)^2$ is further divisible by 2 we have that $p_2 - (\frac{1}{2}p_1)^2$ is divisible by 48. Hence $I_8$ is integral.

\hypertarget{HigherCurvatureCorrection}{}\subsubsection*{{Higher curvature corrections}}\label{HigherCurvatureCorrection}

Possible [[higher curvature corrections]] to 11-dimensional supergravity are discussed in the references listed \hyperlink{ReferencesHigherCurvatureCorrections}{below}.

The first correction is an $R^4$-term at order $\ell^3_{P}$ (11d [[Planck length]]). In \hyperlink{Tsimpis04}{Tsimpis 04} it is shown that part of this is a topological term (total derivative) which related to the [[flux quantization]]-condition of the [[supergravity C-field]].

For effects of higher curvature corrections in a [[Starobinsky model of cosmic inflation]] see \href{Starobinsky+model+of+cosmic+inflation#EmbeddingIntoSupergravity}{there}.

\hypertarget{the_hidden_deformation}{}\subsubsection*{{The hidden deformation}}\label{the_hidden_deformation}

There is in fact a hidden 1-parameter deformation of the Lagrangian of 11d sugra. Mathematically this was maybe first noticed in (\hyperlink{DAuriaFre}{D'Auria-Fre 82}) around equation (4.25). This shows that there is a topological term which may be expressed as

\begin{displaymath}
\propto \int_{X_11} G_4 \wedge G_7
\end{displaymath}
where $G_4$ is the [[curvature]] 3-form of the [[supergravity C-field]] and $G_7$ that of the [[electric-magnetic duality|magnetically dual]] [[C6-field]]. However, (\hyperlink{DAuriaFre}{D'Auria-Fre 82}) consider only topologically trivial (trivial [[instanton sector]]) configurations of the [[supergravity C-field]], and since on them this term is a total derivative, the authors ``drop'' it.

The term then re-appears in the literatur in (\hyperlink{BandosBerkovitsSorokin97}{Bandos-Berkovits-Sorokin 97, equation (4.13)}). And it seems that this is the same term later also redicovered around equation (4.2) in (\hyperlink{Tsimpis04}{Tsimpis 04}).

\begin{quote}%
(hm, check)


\end{quote}
\hypertarget{bps_states}{}\subsubsection*{{BPS states}}\label{bps_states}

The basic [[BPS states]] of 11d SuGra are

\begin{itemize}%
\item the [[M2-brane]]


\item the [[M5-brane]]


\item the [[M-wave]]


\item the [[Kaluza-Klein monopole]]



\end{itemize}
(e.g. \hyperlink{EHKNT07}{EHKNT 07})

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

\begin{itemize}%
\item [[supergravity]]


\item [[12-dimensional supergravity]]


\item 10-dimensional [[type II supergravity]], [[heterotic supergravity]]


\item [[7-dimensional supergravity]]


\item [[5-dimensional supergravity]]


\item [[4-dimensional supergravity]]

\begin{itemize}%
\item [[M-theory on G2-manifolds]], [[G2-MSSM]]


\item [[Freund-Rubin compactification]]



\end{itemize}

\item [[3-dimensional supergravity]]


\item [[supergravity C-field]], [[supergravity Lie 3-algebra]], [[supergravity Lie 6-algebra]]


\item [[Horava-Witten theory]]


\item [[M-theory]]


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



\end{itemize}
[[!include table of branes]]

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

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

That there is a maximal dimension $d = 11$ in which supergravity may exist was found in

\begin{itemize}%
\item [[Werner Nahm]], \emph{[[Supersymmetries and their Representations]]}, Nucl.Phys. B135 (1978) 149 (\href{https://inspirehep.net/record/120988/}{spire}, \href{http://cds.cern.ch/record/132743/files/197709213.pdf}{pdf})

\end{itemize}
The theory was then actually constructed in

\begin{itemize}%
\item [[Eugene Cremmer]], [[Bernard Julia]], [[Joël Scherk]], \emph{Supergravity in theory in 11 dimensions}, Phys. Lett. 76B (1978) 409 ()

\end{itemize}
Formulation in terms of [[supergeometry]] (``superspace formulation'') is in

\begin{itemize}%
\item [[Eugene Cremmer]], S. Ferrara, \emph{Formulation of Eleven-Dimensional Supergravity in Superspace}, Phys.Lett. B91 (1980) 61


\item [[Lars Brink]], [[Paul Howe]], \emph{Eleven-Dimensional Supergravity on the Mass-Shell in Superspace}, Phys.Lett. B91 (1980) 384



\end{itemize}
The history as of 1990s with an eye towards the development to [[M-theory]] is survey in

\begin{itemize}%
\item [[Mike Duff]], chapter I of \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}
The description of 11d supergravity in terms of the [[D'Auria-Fre formulation of supergravity]] originates in

\begin{itemize}%
\item [[Riccardo D'Auria]], [[Pietro Fré]], \emph{[[GeometricSupergravity.pdf:file]]}, Nuclear Physics B201 (1982) 101-140

\end{itemize}
of which a textbook account is in

\begin{itemize}%
\item [[Leonardo Castellani]], [[Riccardo D'Auria]], [[Pietro Fré]], chapters III.8 and V.4-V.11 in \emph{[[Supergravity and Superstrings - A Geometric Perspective]]}, World Scientific, 1991

\end{itemize}
The topological deformation (almost) noticed in equation (4.25) of \hyperlink{DAuriaFre82}{D'Auria-Fre 82} later reappears in (4.13) of

\begin{itemize}%
\item [[Igor Bandos]], [[Nathan Berkovits]], [[Dmitri Sorokin]], \emph{Duality-Symmetric Eleven-Dimensional Supergravity and its Coupling to M-Branes}, Nucl. Phys. B522 (1998) 214-233 (\href{http://arxiv.org/abs/hep-th/9711055}{arXiv:hep-th/9711055})

\end{itemize}
and around (4.2) of \hyperlink{Tsimpis04}{Tsimpis 04}

More recent textbook accounts include

\begin{itemize}%
\item [[Antoine Van Proeyen]], [[Daniel Freedman]], section 10 of \emph{Supergravity}, Cambridge University Press, 2012

\end{itemize}
Discussion of the equivalence of the 11d SuGra [[equations of motion]] with the [[supergravity torsion constraints]] is in

\begin{itemize}%
\item [[Paul Howe]], \emph{Weyl Superspace}, Physics Letters B Volume 415, Issue 2, 11 December 1997, Pages 149--155 (\href{http://arxiv.org/abs/hep-th/9707184}{arXiv:hep-th/9707184})

\end{itemize}
following

\begin{itemize}%
\item A. Candiello, K. Lechner, \emph{Duality in Supergravity Theories}, Nucl.Phys. B412 (1994) 479-501 (\href{http://arxiv.org/abs/hep-th/9309143}{arXiv:hep-th/9309143})

\end{itemize}
Much computational detail is displayed in

\begin{itemize}%
\item Andre Miemiec, Igor Schnakenburg, \emph{Basics of M-Theory}, Fortsch.Phys. 54 (2006) 5-72 (\href{http://arxiv.org/abs/hep-th/0509137}{arXiv:hep-th/0509137})

\end{itemize}
\hypertarget{classical_solutions_and_bps_states}{}\subsubsection*{{Classical solutions and BPS states}}\label{classical_solutions_and_bps_states}

Bosonic solutions of eleven-dimensional supergravity were studied in the 1980s in the context of [[Kaluza-Klein mechanism|Kaluza-Klein]] supergravity. The topic received renewed attention in the mid-to-late 1990s as a result of the [[branes]] and duality paradigm and the [[AdS/CFT correspondence]].

One of the earliest solutions of eleven-dimensional supergravity is the maximally supersymmetric Freund-Rubin background with geometry $AdS_4 \times S^7$ and 4-form [[flux]] proportional to the [[volume form]] on $AdS_4$.

\begin{itemize}%
\item Peter Freund, Mark Rubin, \emph{Dynamics of Dimensional Reduction} Phys.Lett. B97 (1980) 233-235 (\href{http://inspirehep.net/record/154579?ln=en}{inSpire})

\end{itemize}
The radii of curvatures of the two factors are furthermore in a ratio of 1:2. The modern avatar of this solution is as the near-horizon limit of coincident [[M2-branes]].

\begin{itemize}%
\item [[Mike Duff]], [[Kellogg Stelle]], \emph{Multimembrane solutions of D = 11 supergravity} , Phys.Lett. B253 (1991) 113-118 (\href{http://adsabs.harvard.edu/abs/1991PhLB..253..113D}{web})

\end{itemize}
Shortly after the original Freund-Rubin solution was discovered, Englert discovered a deformation of this solution where one could turn on [[flux]] on the $S^7$; namely, singling out one of the [[Killing spinors]] of the solution, a suitable multiple of the 4-form one constructs by squaring the [[spinor]] can be added to the [[volume form]] in $AdS_4$ and the resulting 4-form still obeys the supergravity [[Euler-Lagrange equations|field equations]], albeit with a different relation between the radii of [[curvature]] of the two factors. The flux breaks the [[special orthogonal group|SO(8)]] symmetry of the [[sphere]] to an $SO(7)$ subgroup.

\begin{itemize}%
\item [[Francois Englert]], \emph{Spontaneous Compactification of Eleven-Dimensional Supergravity} Phys.Lett. B119 (1982) 339 (\href{http://inspirehep.net/record/180130}{inSPIRE})

\end{itemize}
Some of the above is taken from \href{http://theoreticalphysics.stackexchange.com/questions/329/modern-avatar-of-englerts-solution}{this TP.SE thread}.

A classification of symmetric solutions is discussed in

\begin{itemize}%
\item [[José Figueroa-O'Farrill]], \emph{Symmetric M-Theory Backgrounds} (\href{http://arxiv.org/abs/1112.4967}{arXiv:1112.4967})


\item Linus Wulff, \emph{All symmetric space solutions of eleven-dimensional supergravity} (\href{https://arxiv.org/abs/1611.06139}{arXiv:1611.06139})



\end{itemize}
Discussion of [[black branes]] and [[BPS states]] includes

\begin{itemize}%
\item [[Kellogg Stelle]], section 3 of \emph{BPS Branes in Supergravity} (\href{http://arxiv.org/abs/hep-th/9803116}{arXiv:hep-th/9803116})


\item [[Francois Englert]], Laurent Houart, [[Axel Kleinschmidt]], [[Hermann Nicolai]], Nassiba Tabti, \emph{An $E_9$ multiplet of BPS states}, JHEP 0705:065,2007 (\href{http://arxiv.org/abs/hep-th/0703285}{arXiv:hep-th/0703285})


\item Andrew Callister, [[Douglas Smith]], \emph{Topological BPS charges in 10 and 11-dimensional supergravity}, Phys. Rev. D78:065042,2008 (\href{http://arxiv.org/abs/0712.3235}{arXiv:0712.3235})


\item Andrew Callister, [[Douglas Smith]], \emph{Topological charges in $SL(2,\mathbb{R})$ covariant massive 11-dimensional and Type IIB SUGRA}, Phys.Rev.D80:125035,2009 (\href{http://arxiv.org/abs/0907.3614}{arXiv:0907.3614})


\item Andrew Callister, \emph{Topological BPS charges in 10- and 11-dimensional supergravity}, thesis 2010 (\href{http://inspirehep.net/record/1221591?ln=en}{spire})


\item A. A. Golubtsova, V.D. Ivashchuk, \emph{BPS branes in 10 and 11 dimensional supergravity}, talk at DIAS 2013 (\href{http://theor.jinr.ru/~diastp/summer13/lectures/Golubtsova.pdf}{pdf slides})


\item Cristine N. Ferreira, \emph{BPS solution for eleven-dimensional supergravity with a conical defect configuration} (\href{http://arxiv.org/abs/1312.0578}{arXiv:1312.0578})



\end{itemize}
Discussion of [[black hole]] horizons includes

\begin{itemize}%
\item [[Jan Gutowski]], [[George Papadopoulos]], \emph{Static M-horizons} (\href{http://arxiv.org/abs/1106.3085}{arXiv:1106.3085})

\end{itemize}
See also

\begin{itemize}%
\item Teng Fei, Bin Guo, Duong H. Phong, \emph{A Geometric Construction of Solutions to 11D Supergravity} (\href{https://arxiv.org/abs/1805.07506}{arXiv:1805.07506})

\end{itemize}
\hypertarget{ReferencesHigherCurvatureCorrections}{}\subsubsection*{{Higher curvature corrections}}\label{ReferencesHigherCurvatureCorrections}

Discussion of [[higher curvature corrections]]:

\begin{itemize}%
\item [[Arkady Tseytlin]], \emph{$R^4$ terms in 11 dimensions and conformal anomaly of (2,0) theory}, Nucl.Phys.B584:233-250, 2000 (\href{https://xxx.lanl.gov/abs/hep-th/0005072}{arXiv:hep-th/0005072})


\item Dimitrios Tsimpis, \emph{11D supergravity at $\mathcal{O}(l^3)$}, JHEP0410:046,2004 (\href{http://arxiv.org/abs/hep-th/0407271}{arXiv:hep-th/0407271})


\item [[Paul Howe]], \emph{$R^4$ terms in supergravity and M-theory} (\href{https://arxiv.org/abs/hep-th/0408177}{arXiv:hep-th/0408177})


\item [[Martin Cederwall]], [[Ulf Gran]], [[Bengt Nilsson]], [[Dimitrios Tsimpis]], \emph{Supersymmetric Corrections to Eleven-Dimensional Supergravity}, JHEP0505:052, 2005 (\href{https://arxiv.org/abs/hep-th/0409107}{arXiv:hep-th/0409107})


\item Anirban Basu, \emph{Constraining gravitational interactions in the M theory effective action}, Classical and Quantum Gravity, Volume 31, Number 16, 2014 (\href{https://arxiv.org/abs/1308.2564}{arXiv:1308.2564})


\item Bertrand Souères, Dimitrios Tsimpis, \emph{The action principle and the supersymmetrisation of Chern-Simons terms in eleven-dimensional supergravity}, Phys. Rev. D 95, 026013 (2017) (\href{https://arxiv.org/abs/1612.02021}{arXiv:1612.02021})



\end{itemize}
and from the [[ABJM model]]:

\begin{itemize}%
\item Damon J. Binder, Shai M. Chester, Silviu S. Pufu, \emph{Absence of $D^4 R^4$ in M-Theory From ABJM} (\href{https://arxiv.org/abs/1808.10554}{arXiv:1808.10554})

\end{itemize}
Discussion in view of the [[Starobinsky model of cosmic inflation]] is in

\begin{itemize}%
\item [[Katrin Becker]], [[Melanie Becker]], \emph{Supersymmetry Breaking, M-Theory and Fluxes}, JHEP 0107:038,2001 (\href{https://arxiv.org/abs/hep-th/0107044}{arXiv:hep-th/0107044})


\item Kazuho Hiraga, Yoshifumi Hyakutake, \emph{Inflationary Cosmology via Quantum Corrections in M-theory} (\href{https://arxiv.org/abs/1809.04724}{arXiv:1809.04724})



\end{itemize}
\hypertarget{scattering_amplitudes_and_effective_action}{}\subsubsection*{{Scattering amplitudes and Effective action}}\label{scattering_amplitudes_and_effective_action}

Computation of [[Feynman amplitudes]]/[[scattering amplitudes]] and [[effective action]] in 11d supergravity:

\begin{itemize}%
\item [[Stanley Deser]], [[Domenico Seminara]], \emph{Counterterms/M-theory Corrections to D=11 Supergravity}, Phys.Rev.Lett.82:2435-2438, 1999 (\href{https://arxiv.org/abs/hep-th/9812136}{arXiv:hep-th/9812136})


\item [[Stanley Deser]], [[Domenico Seminara]], \emph{Tree Amplitudes and Two-loop Counterterms in D=11 Supergravity}, Phys.Rev.D62:084010, 2000 (\href{https://arxiv.org/abs/hep-th/0002241}{arXiv:hep-th/0002241})


\item L. Anguelova, P. A. Grassi, P. Vanhove, \emph{Covariant One-Loop Amplitudes in $D=11$}, Nucl. Phys. B702 (2004) 269-306 (\href{https://arxiv.org/abs/hep-th/0408171}{arXiv:hep-th/0408171})


\item [[Kasper Peeters]], [[Jan Plefka]], Steffen Stern, \emph{Higher-derivative gauge field terms in the M-theory action}, JHEP 0508 (2005) 095 (\href{https://arxiv.org/abs/hep-th/0507178}{arXiv:hep-th/0507178})


\item Hamid R. Bakhtiarizadeh, \emph{Gauge field corrections to eleven dimensional supergravity via dimensional reduction} (\href{https://arxiv.org/abs/1711.11313}{arXiv:1711.11313})



\end{itemize}
\hypertarget{truncations_and_compactifications}{}\subsubsection*{{Truncations and compactifications}}\label{truncations_and_compactifications}

\begin{itemize}%
\item [[Hermann Nicolai]], Krzysztof Pilch, \emph{Consistent truncation of $d = 11$ supergravity on $AdS_4 \times S^7$} (\href{http://arxiv.org/abs/1112.6131}{arXiv:1112.6131})

\end{itemize}
\hypertarget{topology_and_anomaly_cancellation}{}\subsubsection*{{Topology and anomaly cancellation}}\label{topology_and_anomaly_cancellation}

Discussion of [[quantum anomaly]] cancellation and [[Green-Schwarz mechanism]] in 11D supergravity includes the following articles. (For more see at \emph{\href{M5-brane#AnomalyCancellation}{M5-brane -- anomaly cancellation}}).

\begin{itemize}%
\item [[Edward Witten]], \emph{On Flux Quantization In M-Theory And The Effective Action} (\href{http://arxiv.org/abs/hep-th/9609122}{arXiv:hep-th/9609122})


\item [[Edward Witten]], \emph{Five-Brane Effective Action In M-Theory}, J.Geom.Phys.22:103-133, 1997 (\href{https://arxiv.org/abs/hep-th/9610234}{arXiv:hep-th/9610234})


\item [[Dan Freed]], [[Jeff Harvey]], [[Ruben Minasian]], [[Greg Moore]], \emph{Gravitational Anomaly Cancellation for M-Theory Fivebranes}, Adv.Theor.Math.Phys.2:601-618, 1998 (\href{https://arxiv.org/abs/hep-th/9803205}{arXiv:hep-th/9803205})


\item [[Adel Bilal]], Steffen Metzger, \emph{Anomaly cancellation in M-theory: a critical review}, Nucl.Phys. B675 (2003) 416-446 (\href{https://arxiv.org/abs/hep-th/0307152}{arXiv:hep-th/0307152})


\item Samuel Monnier, \emph{Global gravitational anomaly cancellation for five-branes}, Advances in Theoretical and Mathematical Physics, Volume 19 (2015) 3 (\href{https://arxiv.org/abs/1310.2250}{arXiv:1310.2250})


\item Ibrahima Bah, Federico Bonetti, [[Ruben Minasian]], Emily Nardoni, \emph{Class $\mathcal{S}$ Anomalies from M-theory Inflow} (\href{https://arxiv.org/abs/1812.04016}{arXiv:1812.04016})


\item [[Daniel Freed]], \emph{Two nontrivial index theorems in odd dimensions} (\href{http://arxiv.org/abs/dg-ga/9601005}{arXiv:dg-ga/9601005})


\item [[Adel Bilal]], Steffen Metzger, \emph{Anomaly cancellation in M-theory: a critical review} (\href{http://arxiv.org/abs/hep-th/0307152}{arXiv:hep-th/0307152})



\end{itemize}
\hypertarget{description_by_exceptional_generalized_geometry}{}\subsubsection*{{Description by exceptional generalized geometry}}\label{description_by_exceptional_generalized_geometry}

\begin{itemize}%
\item Paulo Pires Pacheco, [[Daniel Waldram]], \emph{M-theory, exceptional generalised geometry and superpotentials} (\href{http://arxiv.org/abs/0804.1362}{arXiv:0804.1362})

\end{itemize}
[[!redirects 11d supergravity]]

[[!redirects D=11 supergravity]]



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