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nLab > nLab General Discussions: AdS/CFT and higher spin gauge theory

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  1.  
    • CommentRowNumber1.
    • CommentAuthorGiotis Mth
    • CommentTimeJan 20th 2015
    • (edited Jan 20th 2015)
    In the AdS/CFT entry of nLab it is stated that

    "Indeed, in (SezginSundell 2002) more detailed arguments are given that the 7-dimensional dual to the 6d theory is a higher spin gauge theory for a higher spin gauge group extending SO(6,2)."

    The way this is phrased it implies that the non abelian strongly coupled 6d (2,0) SCFT is dual to a higher spin gauge theory (i.e. higher spin gravity) in the bulk; this is not true as I understand it. Sezgin and Sundell relate the free 6d theory (i.e. N free tensor multiplets where we have infinity number of conserved currents) to the higher spin gauge theory in the bulk.

    On the other hand the non abelian strongly coupled 6d (2,0) SCFT is dual to 7d gauged supergravity (in the large N limit)
    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJan 20th 2015

    Thanks, should be fixed. Feel invited to edit the entry. Myself, I have zero time right this moment.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJan 20th 2015

    I have added the qualifier “free”. No time for more right now. Thanks again for catching this.

    • CommentRowNumber4.
    • CommentAuthorGiotis Mth
    • CommentTimeJan 21st 2015
    I think this is adequate for the moment; when I find time I will check too if something needs to be clarified further.
    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJan 21st 2015

    Certainly the whole entry could do with much more. The state it is in (as with so many other entries) is the state that time and energy was available for, not the intended final state.

    Thanks for all your help! Will be much appreciated.

    • CommentRowNumber6.
    • CommentAuthorGiotis Mth
    • CommentTimeJan 29th 2015
    I read this excerpt again and it seems I fail to understand this implied connection between the Higher Spin group of Vasiliev’s HS gravity and Spin (6,2). It would be very helpful if the author could shed more light on this assertion.

    I also noticed that this connection to Sezgin, Sundell paper is missing in http://arxiv.org/abs/1201.5277v1
    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJan 29th 2015
    • (edited Jan 29th 2015)

    We are talking about this sentence, is that right? That’s just a pointer to what Sezgin-Sundell say, specifically in their section 7. The sentence is not making any claim beyond saying that they argue what they argue are.

    I added that pointer at some stage, when I thought it was suggestive of something. I don’t know if I still think so, and if there is something troubling about this pointer I won’t object to changing it or removing it, but presently I fail to see what troubles you about it.

    But, as I said before. If you have the energy, please feel invited to hit EDIT on the entry and improve what you feel you can improve.

    • CommentRowNumber8.
    • CommentAuthorGiotis Mth
    • CommentTimeJan 29th 2015
    It troubles me because the implications of this sentence are quite severe as I understand it at least. To tell you the truth I was quite surprised when I read it since (again as I see it) it implies that somehow the theory of free SU(N) valued d = 6, N = (2, 0) tensor singletons is related (dual?) to the interacting non abelian d = 6, N = (2, 0) theory. This is huge.

    In any case the Higher spin group in the Sezgin, Sundell paper is applicable not only in AdS7 but in the AdS5, AdS4 cases too.

    So if there is no real justification with your permission I will delete it. I will also delete the relevant statement in the references.
    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeJan 29th 2015

    So you are doubting the claim by Sezgin-Sundell?

    • CommentRowNumber10.
    • CommentAuthorGiotis Mth
    • CommentTimeJan 29th 2015
    Not at all (what it is described in Sezgin-Sundell paper is pretty standard), I doubt what it is implied by this sentence as I explained above.
    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeJan 30th 2015

    Then why do you want to delete the reference?

    Come on, we are going on about a single short sentence that does nothing but point to this reference. If the fine detail of the sentence troubles you, then change it. The nLab page deserves a pointer to section 7 in Sezgin-Sundell, regarding their

    We conjecture that the free singleton theory at the IR fixed point mentioned above is the holographic dual of an hs(8∗|4) gauge theory which admits a consistent truncation to the massless hs(8∗|4) gauge theory in D = 7 described in Section 2.2

    • CommentRowNumber12.
    • CommentAuthorGiotis Mth
    • CommentTimeJan 30th 2015
    • (edited Jan 30th 2015)
    I don’t have a problem to put a reference to the Sezgin-Sundell paper but then please delete the phrases:

    “Indeed, in (SezginSundell 2002, section 7) more detailed arguments are given that”

    and then put a reference to SezginSundell 2002.

    In the references remove the phrases:

    “In, fact in”

    and

    “arguments are given that the 7d theory is a higher spin gauge theory extension of SO(6,2).”

    Using these phrases you couple the discussion and findings of the strongly coupled 6d (2,0) SCFT (i.e. what people have in mind when they are referring to the 6d(2,0) SCFT) to the 6d free SCFT and thus the end result is misleading.

    These are two different theories. Sezgin-Sundell paper examines the free 6d SCFT which is dual to HS gravity in the bulk. Moreover by coupling the two discussions with these phrases you are using the Sezgin-Sundell paper to justify the results described above regarding Spin (6,2) etc; these two are unrelated (as I understand it at least).

    Finally Sezgin-Sundell paper is quite general; the results about the free SCFTs hold not only for AdS7/CFT6 but for AdS5/CFT4 and AdS4/CFT3 too. So you must include the relevant references to the paper in these chapters too (with accompanyining text) if you want to be consistent.
    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeJan 30th 2015

    The higher spin algebra which they use is an extension of SO(6,2)SO(6,2) and that “the 7-dimensional dual to the free 6d theory is a higher spin gauge theory for a higher spin gauge group extending SO(6,2).” is just what they say in that quote from #11

    • CommentRowNumber14.
    • CommentAuthorGiotis Mth
    • CommentTimeJan 30th 2015
    Correct but they don't link this to the strongly coupled 6d SCFT analysis as you do (using the aforementioned phrases). The strongly coupled 6d is a different theory.
    • CommentRowNumber15.
    • CommentAuthorUrs
    • CommentTimeFeb 1st 2015
    • (edited Feb 1st 2015)

    Sorry, I really don’t see where you see this claim. There is a sentence that does nothing but point to their article, saying: look, they show this, related to the role of the conformal group.

    I think we have now spent enough time exchanging comments on one single sentence that does nothing but point to the literature. From here there is only one way forward: if you want to see a more comprehensive discussion on that page (in #12 where you say “consistent” you must mean “complete” or “comprehensive”) you have two options: either wait for somebody to find the time and energy, or offer something yourself.

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