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A stub for M-theory. What’s supposed to be so mysterious about it? Is it that people don’t even know what form it would take?
Yes, that’s the problem. What one has is this incomplete diagram
$\array{ ??? &\stackrel{effective QFT}{\to}& 11d Supergravity \\ \downarrow && \downarrow^{\mathrlap{dimensional reduction}} \\ StringTheory &\stackrel{effective QFT}{\to}& 10d Supergravity }$and some indications that indeed there is a way to complete it, because some facets of the bottom left and top right entry do seem to come from a common source in the top left.
But beyond these indications, there has never been much actual progress with actually completing the diagram. Most articles that mention the word “M-theory” refer essentially to the top right item.
I have expanded the entry a bit. Needless to say, this is not doing the topic justice yet. But is maybe a start.
added some more pointers to references at M-theory
added to the References a pointer to the conference talk video where Witten announces the strong coupling conjecture
(Thanks to Cliff Harvey! I still need to find the precise referencing data.)
Added more early quotes on the problem of formulating M-theory being open:
Duff 96, totality of Section 6:
The overriding problem in superunification in the coming years will be to take the Mystery out of M-theory, while keeping the Magic and the Membranes.
Duff 98a, last paragraph (p. 6):
Despite all these successes, physicists are glimpsing only small corners of M-theory; the big picture is still lacking.
Indeed future historians may judge the late 20th century as a time when theorists were like children playing on the seashore, diverting themselves with the smoother pebbles or prettier shells of superstrings while the great ocean of M-theory lay undiscovered before them.
we are only just beginning to scratch the surface of the ultimate meaning of M-theory, and for the time being therefore, M stands for Magic and Mystery too.
continued the list of quotes on the open problem with quotes on the missing derivation/formulation of the nonabelian DBI action:
A key ingredient of M-theory is supposedly the physics of intersecting branes with gauge enhancement in their worldvolume super Yang-Mills theory/DBI field theory. But the actual derivation or even formulation of the expected non-abelian DBI action remains open:
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The explicit construction of such an action is a difficult problem that has been studied extensively (starting with [17]), but is not yet completely settled.
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Several attempts to generalize the Born-Infeld action describing on D-brane to non-Abelian action describing a stack of them have been made. The proper (perhaps closed) form of it is however not known up to date.
added one more such quote:
For a system of multiple D$p$-branes, the world-volume action is much less well understood than for a single brane. The extension of $[$ the super Yang-Mills action $]$ to a full super-symmetric or κ-symmetric nonabelian Born-Infeld action is not known.
$[$the proposal by Tseytlin 97$]$ has not yet been derived from any more fundamental principles
added another quote highlighting the open problem, now related to the common argument for the M5-brane anomaly cancellation:
$[$…$]$ the solution is not so clear. $[$The established procedure$]$ will not work for the M5-brane. $[$…$]$ something new is required. What this something new is, is not a priori obvious. $[$…$]$ $[$This is$]$ a daunting task. To my knowledge no serious attempts have been made to study the problem.
$[$The proposal of FHMM 98$]$ probably should not be viewed as a final understanding of the problem. One would eventually hope for a microscopic formulation of M-theory which makes some of the manipulations $[$proposed in FHMM 98$]$ appear more natural.
You seem to be refraining on this page from saying you have the answers to some of these open problems, such as M5-brane anomaly cancellation (#11).
I think the last update you gave on the problem in (#12) was over here. How’s that coming along?
Once the article is has been accepted, I’ll mention it there. As you will have seen, we have split off the M5-argument to a separate article. Am finalizing that right now, therefore collecting these quotes now.
added further quotes from Duff on the open problem:
Duff interview at M-Theory-Mathematics 2020:
(06:59) But the matrix model itself was not all of M-theory; it was a corner of M-theory, and it told us certain interesting things, but there were interesting things about M-theory that it didn’t tell us.
(07:13) I think we are still looking, in fact, for what M-theory really is.
(07:19) We have a patchwork picture. We understand various corners. But the overarching big picture of M-theory is still waiting to be discovered, in my view.
(08:12) M-theory in 1995 was very promising, and it’s taught us a lot about the fundamental interactions; but the final theory is still not with us.
(12:46) I wouldn’t like to predict what the ultimate picture of M-theory will be; I imagine it will be something quite different from what we can imagine now.
(16:36) That’s why I think M-theory is not yet in a mature enough stage for us to make falsifiable predictions.
(16:44) We don’t understand the theory sufficiently well yet to do so.
added yet one more in the list of quotes explicitly stating open problems:
The M5-brane theory remains an important open problem.
(You would think there must be dozens of quotes to this extent. But while everyone knows this, few authors state it explicitly this way. )
added (here) one more item to the list of quotes highlighting the open problem of fomulating the theory (from CGNT 04):
Our understanding of M-theory is still very limited, mainly due to the lack of powerful methods to probe it at the microscopic level. One approach to encoding information about M-theory is through its low energy effective field theory. $[...]$ The ultimate goal is to be able to derive the higher derivative corrections, e.g. by means of a microscopic version of M-theory. Since this is not yet possible, our aim here is instead to solve the superspace Bianchi identities in order to obtain the most general form such correction terms can take restricted only by supersymmetry and Lorentz invariance in eleven dimensions. To what extent such an approach can capture main features of M-theory is an interesting question to which we have no answer at this point.
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