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Atrium > Mathematics, Physics & Philosophy: Hypothesis H and Matrix models

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    • CommentRowNumber1.
    • CommentAuthorSpacenumbat
    • CommentTimeDec 31st 2021
    Hi,

    I am a layperson who has read all the popular books about String theory and my hobby right now is trying to get a better sense of what is happening at the frontier. I have been reading here that Hypothesis H could lead to a full understanding of M-theory. I have also been reading recently about matrix models. Wikipedia says that the authors BFSS claim their matrix model is exactly equivalent to M-theory. I also read recently that the IKKT matrix model, which models the Type IIb string theory and not the full m-theory, has been claimed to dynamically compactify the extra dimensions making our spacetime emergent, and thereby avoiding the problem of the landscape of vacua of string theory.

    My question is whether these ideas are in conflict or are they compatible. If Hypothesis H is true and it completes m-theory, would it render the IKKT matrix model invalid or obsolete or, conversely, is it plausible that Hypothesis H would independently reproduce the IKKT model's result of spontaneously compactifying the extra dimensions.

    I have more questions too, but I will leave those for another thread. Thank you so much for your time!
    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeDec 31st 2021
    • (edited Dec 31st 2021)

    It should all be compatible in the end, keeping in mind the limits of available proposals.

    For instance, we found that:

    • the Green-Schwarz action functional for the supermembrane (whose regularized quantization is the BFSS matrix model) is part of the rational equivariant Cohomotopy data postulated by Hypothesis H (this is Prop. 6.10 in Sec. 6.2 of arXiv:1805.05987);

    • the quantum ground states of the BMN version of the BFSS matrix model are plausibly seen among the quantum states of M-theory according to Hypothesis H – this is the content of Sec. 4.9 of arXiv:1912.10425,

      I touch upon this in my recent talk Some Quantum States of M-Branes under Hypothesis H.

    But one should note that there are still limitations on both sides:

    (1) The BFSS matrix model is thought to see some corner of M-theory, but not the full thing (references here). For instance the BMN matrix model is a generalization/deformation of the BFSS model which clearly sees a different corner of M-theory.

    (2) We haven’t really pushed for a full definition of M-theory via Hypothesis H just yet. Most of the checks we made so far concern differential-topological conditions of the flux fields over classical background spacetimes. From there we started exploring the quantum implications of the Hypothesis in arXiv:1912.10425 and arXiv:2105.02871, but this is not meant to be complete yet.

    Notably, these discussions of Hypothesis H concern only the C-field so far, ignoring the field of (super-)gravity. It is hence clear that this cannot be the full picture yet, and that there is more detailed implications of Hypothesis H to be worked out. We think we know how to include the metric field (this is briefly indicated on slide 14 here) but analyzing this in detail remains to be done.

    • CommentRowNumber3.
    • CommentAuthorSpacenumbat
    • CommentTimeDec 31st 2021
    This is great, thank you very much!

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