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The IKKT matrix model isn’t all that background independent: these matrix models have a background metric in their Lagrangian and do remember at least the asymptotic symmetries of that background (which may or may not be good enough). For example, the BFSS matrix model and the BMN matrix model are derived in different backgrounds (Minkowski and pp-wave, respectively) and their spectrum remembers this (BMN has bound SUSY ground states, BFSS does not).
The problem with LQG is that, after declaration of radical ambition, nothing it made to work (Pysics.SE:a/360010).
It’s still all up for grabs. But possibly best not to wish too hard for it: What has hurt communities is trying to hard-wire their psychological preconceptions of what quantum spacetime should be into their theories, instead of letting the theory tell them.
Generally, if a would-be theory of quantum gravity has either
or
and preferably both
then it’s worth taking note of as a hint towards humanity’s quest to solve this riddle.
But if it has (b) no discernible output while being based on (a) a crazy left turn at step one, then it is a waste of time.
That said, I do think that there is much room left to analyze the IKKT matrix model in more depth, notably in more mathematical sophistication. (Back in the golden 90s one could see Alain Connes talk about IKKT (arXiv:hep-th/9711162) highlighting that its eponymous matrices are hardly those but must be understood as operators on a Hilbert space, making matrix model theory a topic in operator algebra.)
Another evident suggestion that remains underappreciated is that in holographic QCD baryons are modeled by D-branes and hence multiple baryons ought to be modeled by the respective “nuclear matrix model”.
There are several promising loose ends like this sitting around waiting to be picked up, while the ST community is lost in the Swampland (to pick up Banks’ ranting from arXiv:1910.12817).
But that’s okay, this gives us time to put up the machinery for the next serious attack…
Banks argues that the corners of M-theory that have a decent theoretical underpinning – such as the matrix models – look decidedly different from the assumptions that the bulk of the string-pheno community is running their business on.
What this means for string-pheno-done-right will only be answerable once its done right – which in turn will require formulating more of the M-theory first. It’s a long way ahead. (See also Duff 2020 around 16:36.)
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