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    • CommentRowNumber1.
    • CommentAuthorSpacenumbat
    • CommentTimeJan 17th 2022
    In Brian Greene's book The Fabric of the Cosmos (2004) he suggests the possibility that String Theory and Loop Quantum Gravity may be two attempts to construct the same theory from very different starting points. He goes on to express the hope that a background independent formulation of String Theory could reconcile it with the atomized spacetime found in LQG.

    Wanting to know if any progress has been made in this area I searched and found this old forum post by Urs comparing the IKKT matrix model of the type IIb string theory to Loop Quantum Gravity. He says that both display 'radical background independence'

    Have the prospects for this type of research changed since 2003? What are the prospects for the IKKT model and, more ambitiously, the unification of LQG and String Theory?
    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJan 17th 2022
    • (edited Jan 17th 2022)

    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).

    • CommentRowNumber3.
    • CommentAuthorSpacenumbat
    • CommentTimeJan 17th 2022
    So is the concept of discretizing / quantizing spacetime itself flawed?
    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJan 18th 2022

    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

    • (a) a compelling input


    • (b) a fascinating output,

    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.

    • CommentRowNumber5.
    • CommentAuthorSpacenumbat
    • CommentTimeJan 18th 2022
    Okay that makes sense.
    Thanks Urs!
    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJan 18th 2022

    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…

    • CommentRowNumber7.
    • CommentAuthorSpacenumbat
    • CommentTimeJan 18th 2022
    So that Tom Banks paper is arguing that the String Landscape as well as the Inflationary multiverse are not real (or at least not well founded theoretically). Without the multiverse, how then does one explain fine tuning?
    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJan 18th 2022
    • (edited Jan 18th 2022)

    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.)