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  Is the conjecture about $E(11)$ and M-theory (West's conjecture) generally accepted?

+ 6 like - 0 dislike

I was reading this paper by West, in which it is argued that:

Eleven dimensional supergravity can be described by a non-linear realisation based on the group $E\left(11\right)$

From which they conjecture that $ E\left(11\right) $ can be related to M-theory, too. This seems rather weird to me, given that $E\left(11\right) $ is a rather unwieldy group, given that it has a cartan determinant of $-2$. The cartan matrix of the group is as follows:

$$\left[ {\begin{array}{*{20}{c}} 2&{ - 1}&{}&{}&{}&{}&{}&{}&{}&{}&{} \\ { - 1}&2&{ - 1}&{}&{}&{}&{}&{}&{}&{}&{} \\ {}&{ - 1}&2&{ - 1}&{}&{}&{}&{}&{}&{}&{ - 1} \\ {}&{}&{ - 1}&2&{ - 1}&{}&{}&{}&{}&{}&{} \\ {}&{}&{}&{ - 1}&2&{ - 1}&{}&{}&{}&{}&{} \\ {}&{}&{}&{}&{ - 1}&2&{ - 1}&{}&{}&{}&{} \\ {}&{}&{}&{}&{}&{ - 1}&2&{ - 1}&{}&{}&{} \\ {}&{}&{}&{}&{}&{}&{ - 1}&2&{ - 1}&{}&{} \\ {}&{}&{}&{}&{}&{}&{}&{ - 1}&2&{ - 1}&{} \\ {}&{}&{}&{}&{}&{}&{}&{}&{ - 1}&2&{} \\ {}&{}&{ - 1}&{}&{}&{}&{}&{}&{}&{}&2 \end{array}} \right]$$

So, is this paper well-accepted in the string community?

asked Aug 14, 2013 in Theoretical Physics by dimension10 (1,985 points) [ revision history ]
edited Apr 26, 2015 by dimension10

Submission for West's paper: E_11 and M Theory.

2 Answers

+ 5 like - 0 dislike

The conjecture -- in the somewhat vague form as it is given -- is a pretty straightforward, compelling extrapolation of a long list of known facts about U-duality groups (see there). Moreover, West, Nicolai, Kleinschmidt and others have given long and detailed discussion for how to match plenty of main structural aspects of 11d sugra and the M-branes into various elements of the level decomposition of the E-series Kac-Moody Lie algebras. Concrete discussion of symmetry groups in supergravity routinely compares to structures in \(E_{11}\).Moreover, all the "lower" U-duality groups \(E_{n(n)}\)are all known to act via their canonical action on their coset by their maximal compact subgroups (called "non-linear realization"), and hence the statement that "M-theory can be described by a non-linear realisation based on the group \(E_{11(11)}\)" is not very far-fetched at all, given all that is known. On the other hand, as far as I can see, it remains unclear just what "can be described" will turn out to mean. But that the low level decompositions of \(E_{11(11)}\) happen to know a lot about what is otherwise known about M-theory (which is much in itself, but relatively little as to what is probably waiting to be understood) is established. The remaining question is what exactly this now implies.

answered May 24, 2014 by Urs Schreiber (6,095 points) [ revision history ]
edited Jul 13, 2014 by Arnold Neumaier
+ 4 like - 0 dislike

I cannot speak to whether or not $E_{11}$ is "ugly" but if you see, e.g. arXiv:1308.1673, West's paper is referred to as an "ambitious" proposal. Moreover, West's paper has been cited over 250 times, which indicates it's fairly well-known. (This would be classified as "famous" according to inspirehep.net.)

This post imported from StackExchange Physics at 2014-03-07 16:35 (UCT), posted by SE-user sujeet
answered Aug 14, 2013 by sujeet (40 points) [ no revision ]

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