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

Question

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?

Comments

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

Answer 1

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.

Answer 2

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