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added also references on black holes from BFSS matrix theory. Am adding these same references also at black holes in string theory
The entry should have a list of pointers to references on the – by and large open – problem of a sensible ground state in the BFSS model. Have added at least this pointer here, which is a new attempt, and the article has pointers to previous attempts:
added pointer to
which looks interesting. Also touched random matrix theory.
In the 90s there was much excitement about the BFSS model, as people hoped it might provide a definition of M-theory.
There’s also the use of ’is supposed to’, ’was argued to’, etc., suggesting goals weren’t met. Would it be possible to add a word about the obstacle(s) that they encountered?
The BFSS matrix models clearly sees something M-theoretic, but just as clearly it is not the full answer. Notably it needs for its definition an ambient Minkowski background, a light cone limit and a peculicar scaling of string coupling over string length, all of which means that it pertains to a particular corner of a full theory.
Then even assuming that in this corner all the crucial cohomological aspects of branes (K-theory charges, etc.) are secretly encoded in the matrix model, magically, none of this is manifest, making the matrix model spit out numbers about a conceptually elusive theory in close analogy to how lattice QCD produces numbers without informing us about the actual conceptual nature of hadron physics.
And then there are technical open issues, such as the open question wether the theory has a decent ground state the way it needs to have to make sense (here).
Here a similar assessment in the words of Greg Moore, from pages 43-44 of his Physical Mathematics and the Future (here):
A good start $[$on defining M-theory$]$ was given by the Matrix theory approach of Banks, Fischler, Shenker and Susskind. We have every reason to expect that this theory produces the correct scattering amplitudes of modes in the 11-dimensional supergravity multiplet in 11-dimensional Minkowski space - even at energies sufficiently large that black holes should be created. (This latter phenomenon has never been explicitly demonstrated). But Matrix theory is only a beginning and does not give us the whole picture of M-theory. The program ran into increasing technical difficulties when more complicated compactifications were investigated. (For example, compactification on a six-dimensional torus is not very well understood at all. […]). Moreover, to my mind, as it has thus far been practiced it has an important flaw: It has not led to much significant new mathematics.
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.
Presumably a good M-theory will explain whatever success the BFSS model has.
Certainly. Coming from actual M-theory, the BFSS matrix model should appear from the actual M2-brane, along the lines explained orgininally by Nicolai et al (here)
From that reference:
Despite the recent excitement, however, we do not think that M(atrix) theory and the $d= 11$ supermembrane in their present incarnation are already the final answer in the search for M-Theory, even though they probably are important pieces of the puzzle. There are still too many ingredients missing that we would expect the final theory to possess. For one thing, we would expect a true theory of quantum gravity to exhibit certain pregeometrical features corresponding to a “dissolution” of space-time and the emergence of some kind of non-commutative geometry at short distances; although the matrix model does achieve that to some extent by replacing commuting coordinates by non-commuting matrices, it seems to us that a still more radical departure from conventional ideas about space and time may be required in order to arrive at a truly background independent formulation (the matrix model “lives” in nine flat transverse dimensions only). Furthermore, there should exist some huge and so far completely hidden symmetries generalizing not only the duality symmetries of extended supergravity and string theory, but also the principles underlying general relativity.
added pointer to today’s
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