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Holography without string theory (new paper by Don Marolf)

  1. Aug 11, 2013 #1

    marcus

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    This was just posted on arxiv. It seems to be of general interest so here's a thread in case anyone wants to discuss it.
    http://arxiv.org/abs/1308.1977
    Holography without strings?
    Donald Marolf
    (Submitted on 8 Aug 2013)
    A defining feature of holographic dualities is that, along with the bulk equations of motion, boundary correlators at any given time t determine those of observables deep in the bulk. We argue that this property emerges from the bulk gravitational Gauss law together with bulk quantum entanglement as embodied in the Reeh-Schlieder theorem. Stringy bulk degrees of freedom are not required and play little role even when they exist. As an example we study a toy model whose matter sector is a free scalar field. The energy density (ρ) sources what we call a pseudo-Newtonian potential (Φ) through Poisson's equation on each constant time surface, but there is no back-reaction of Φ on the matter. We show the Hamiltonian to be essentially self-adjoint on the domain generated from the vacuum by acting with boundary observables localized in an arbitrarily small neighborhood of the chosen time t. Since the Gauss law represents the Hamiltonian as a boundary term, the model is holographic in the sense stated above.
    13 pages
     
  2. jcsd
  3. Aug 12, 2013 #2

    MTd2

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  4. Aug 12, 2013 #3

    marcus

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    He he, yes. The Dreaded Yasha!

    MTd2, what makes this paper extra significant is Marolf's stature and his dual role in the String and
    Quantum Gravity research communities.

    He has been a longtime close collaborator with top people at KITP-Santa Barbara. I guess everybody knows that. You could think of him as a string researcher because of his many collaborative papers. But on the other hand he has also co-authored with Abhay Ashtekar and is in the acknowledgments of a number of Loop papers. I think of him as an independent QG mathematician who works interesting stuff. Also I think he was the main organizer in charge of GR19 Mexico City, in 2010. This is a big international triennial conference that can get say 900 participants, held by the GRG (General Relativity and Gravitation organization.) So this is somebody with deep knowledge broad experience and major reputation. Who also seems to be able to cross lines and ignore factional differences.

    For me that carries some weight. So when he says about holo dualities that:
    We argue that this property emerges from the bulk gravitational Gauss law together with bulk quantum entanglement as embodied in the Reeh-Schlieder theorem. Stringy bulk degrees of freedom are not required and play little role even when they exist it matters who is saying it as well as what the supporting argument is.
     
    Last edited: Aug 12, 2013
  5. Aug 12, 2013 #4

    marcus

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    Here are a couple of interesting quotes from
    http://arxiv.org/abs/1308.1977

    ==Marolf, Introduction page 1==
    Holographic dualities [1, 2] are settings where one theory (the bulk) is dual to a second theory (the dual field theory, or DFT) living on a lower dimensional spacetime. In simple cases the DFT spacetime can be identified with the boundary of the bulk, and local DFT operators can be identified [3] with boundary limits of bulk operators. For this to be a true duality any bulk operator must, at least in principle, be expressible in terms of DFT operators. This suggests that all bulk operators are in fact determined by their boundary values.

    While this property may sound striking at first, in a free bulk quantum field theory it is actually straightforward to show that all bulk operators can be written in terms of their boundary values. The point is that signals in the bulk eventually travel outward and reach the boundary.1 The free result may then be corrected perturbatively for bulk interactions which, in familiar examples, corresponds to performing a 1/N expansion in the DFT [11, 12, 13, 14, 15, 16, 17].

    The interesting point about holographic theories is that they take this observation one step further. Since the DFT is a self-contained theory which evolves deterministically under its own Hamiltonian...
    ==endquote==

    ==Marolf, Conclusions page 9==
    We have stressed that our model contains no stringy degrees of freedom. We conclude that stringy dynamics is not required for information holography and suggest that, even when they are present in holographic theories, such degrees of freedom may play little direct role. It was of course already known that other critical properties of the DFT are not directly connected to strings. These include the vanishing of commutators at spacelike separation (i.e., locality, which follows from a quantum version of [49]) and the existence in appropriate cases of a DFT stress tensor [3]. Thus our work here strengthens the argument that any UV complete theory of gravity will be holographic, even if it contains no strings.10

    On the other hand, the existence of bulk strings is intimately related to the gauge theoretic nature of the DFTs that arise in known examples [34]...
    ==endquote==
     
  6. Aug 13, 2013 #5

    MTd2

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    It seems more and more that holography is an extension of quantum mechanics and that gravity is part of this extension, like a Fourier transform is part of QM.
     
  7. Aug 13, 2013 #6

    marcus

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    That sounds like a pregnant thought. I wish I understood better what you have in mind.

    You may be getting more out of the paper than I am--for me the message is mostly just that AdS/CFT and related stuff are not specifically a part of String research. They are common mathematical property shared by everybody--and do not bear the String "brand". This helps to clarify the map of research terrain for me. So the import of the paper is for me relatively simple.

    For one thing I see a considerable number of Loop researchers working with the Oeckl GBF (general boundary formulation) of general covariant quantum theory. I see the GBF as possibly replacing Dirac quantization.
    It offers a naturally general covariant way to do QFT and QSM (quantum statistical mechanics). the papers of Bianchi, Haggard and Rovelli (in various combinations) highlight the importance of GBF.

    And in GBF the Hilbertspace (or the corresponding operator algebra) consists of states that describe the boundary of a 4d region containing the process.
    But this precisely parallels what is done in spinfoam QG! where one focuses on the spinnetwork boundary surrounding the spinfoam bulk, and one aims to calculate the amplitude of the boundary. It is like a transition amplitude except that the approach is made general covariant by using a general boundary instead of specified initial and final patches.

    So what I think I see is a convergent evolution which is rapidly bringing forward a kind of boundary formalism for general covariant quantum theory (whether it is QFT, or QSM, or spin foam, or one of the several types of holographic duality that we hear about). this is just my impressionistic take on it, and not an especially subtle one, so I would like to understand better how it looks to you.

    ====================
    EDIT TO REPLY TO the next post, by DimReg: I know what you mean, GBF does belong in a different thread, if one is going to get into a proper discussion of it. I'm glad to hear you also suspect GBF might be better for general covariant quantization than the Dirac recipe with it Hamiltonian constraint!
     
    Last edited: Aug 13, 2013
  8. Aug 13, 2013 #7
    If I remember my physics history correct... wasn't the holographic principle first proposed outside of string theory? (Or at least, wikipedia seems to imply that). If that's right, this paper doesn't seem to say anything far from the original spirit of the principle. Though of course, it's still a shocking idea given the current prevailing opinions in physics.

    That would be a cool way to see holography realized in LQG; as a fundamental part of the construction of the theory. I also think GBF might be better for general covariant quantization than Dirac quantization, but I feel like that fits into a different thread.
     
  9. Aug 14, 2013 #8

    MTd2

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    For one thing, the boundary of a region can effectively weight its content. If it saturates, it becomes a black hole. Also, on the other hand, the boundary can describe the events inside it.
    So, the boundary can both capture the mass energy and its fields without bringing together gravity and geometry. The easiest way to see this it is now geometry is now a defined place, the boundary, while gravity can only affect it non locally, through the bulk.

    So, like a Fourier transform in quantum mechanics, you go from local physics, x, to, non local, p.In GR, you only deal with x, where p can only obtained with a local clock and rod, so you cannot find a quantum p within GR without changing something fundamental of the theory.

    With holography, you can do that transform. But the price you pay it is that gravity is not anymore quantizable object, but part of the quantization procedure.
     
  10. Aug 15, 2013 #9

    marcus

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    I think that's right, by Gerard 't Hooft wasn't it?

    I know what you mean :biggrin:


    Really cool! I responded to earlier (edit tacked onto post#6)
     
  11. Aug 15, 2013 #10

    marcus

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    I'm partly understanding what you have in mind--thanks for the clarification! It is a difficult idea to express, so it would be helpful to hear more explanation. I understand the part about Fourier transform connecting local description with non-local. But I'm not sure I understand "now geometry is now defined place". Which is analogous to the non-local description? the boundary field or the bulk field?

    BTW Mitchell had an interesting comment about the Marolf paper on Woit's blog:
    Mitchell Porter says:
    August 15, 2013 at 1:33 am
    I am still digesting Marolf’s paper but it seems a little dodgy. It does not talk about holographic *duality* at all – i.e. the equivalence between a theory in the bulk and another theory on the boundary. Instead, it is (I think) an argument that a general quantum state in the bulk theory can be constructed just using bulk operators from the boundary.

    To understand what that means, we need to distinguish between operators in a separate theory defined on the boundary, as in AdS/CFT, and operators in the bulk theory which pertain to bulk observables near the boundary. In the latter case we are talking only about one theory, called the bulk theory, but we concern ourselves with operators in that theory which are associated with the edge of the bulk...​
    http://www.math.columbia.edu/~woit/wordpress/?p=6192&cpage=1#comment-159015

    In fact I do not think Marolf's paper is at all "dodgy" in this regard! :smile: What Marolf is showing is a stronger form of holographic duality, not a weaker. Namely one where the field on the boundary is an extension of the bulk field.

    So you have less freedom in how the boundary field (what he calls the DFT, dual field theory) is defined and *nevertheless* he argues there is an holographic duality.

    (which as he points out does not require involving any string degrees of freedom).

    So we'll have to see if this stands up in court. :biggrin: It could be that there's a flaw in the argument or the proof is incomplete. However that may be, the claim itself, I would say, is not "dodgy". Instead it is indeed quite a strong one.
     
    Last edited: Aug 15, 2013
  12. Aug 15, 2013 #11

    fzero

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    I would say that Mitchell is pointing out something important, but perhaps isn't giving the whole story. My first impression too was that Marolf is not making any big distinction between the properties of the bulk and boundary theories. The original holographic proposals were not very specific about this either, but the string examples are extremely specific.

    In fact, a key feature of matrix theory and AdS/CFT is that the lower-dimensional theory is nongravitational, but nevertheless a gravitational theory emerges in the bulk. If Marolf is indeed saying that the "field on the boundary is an extension of the bulk field" (your words), it is unclear how the boundary theory might become nongravitational.

    Note that this isn't just a case of limits. In AdS/CFT it is clear that there is a limit where stringy and gravitational corrections turn off. However the duality remains when we do not take this limit and the gauge theory perfectly well describes bulk gravity without introducing gravity explicitly.

    However, the use of limits does illustrate that string degrees of freedom are not always relevant. In the limit of weak gauge coupling and large 't Hooft coupling, the bulk theory is just weakly-coupled supergravity. This is not a limit where the degrees of freedom of the gauge theory change in any significant way (leaving aside questions of symmetry breaking and gauge theory vacuum, etc). It would obviously be of interest to see a connection between the boundary and bulk in this limit that is independent of stringy considerations, but I wouldn't say that Marolf's toy model is rich enough to extrapolate from.

    It may be that there is some more general version of holography, but it is very hard to see how Marolf would explain the versions that we already know of. Of course, many examples of boundary theories that are themselves gauge theories will inevitably involve QCD-type strings (at least in confining phases), so it is very hard to see how the bulk theory itself would not have some sort of stringy objects (again, at least in certain phases). Marolf does make a short comment about this connection between strings and gauge theories in a later part of the paper.
     
    Last edited: Aug 15, 2013
  13. Aug 15, 2013 #12

    marcus

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    Thanks fzero! I think its very valuable to have your perspective on this. Unfortunately I have to go to doctor's appt. almost immediately, so cannot properly examine or respond. Back later this afternoon.
    EDIT: Back now and had time to look over your post. I think what I was calling a feature you may be calling a bug :biggrin: They find that the bulk gravity theory is holographic even within a more restricted class of boundary DFT. Logically I think that counts as a stronger conclusion in the sense that you are allowed less freedom in choosing the Dual Field Theory. This was my point in post#4.
    You may find it unsatisfactory because it doesn't include some interesting DFT examples, but let's give Marolf time and he may broaden the result. Basically he is able to find ONE dual field theory (of a specific sort) that works, and so he proves his point. But there may well be OTHER types of DFT that work as well (without string involvement) and we may hear more about that later.

    Here's what I think is the important thing for now. As was said in the conclusions:
    Thus our work here strengthens the argument that any UV complete theory of gravity will be holographic, even if it contains no strings.
     
    Last edited: Aug 15, 2013
  14. Aug 15, 2013 #13

    fzero

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    I am at a loss to determine how the pseudo-Newtonian model considered by Marolf in any way resembles a UV complete theory of gravity, so I don't see how one can draw a strong conclusion by studying it. The toy model doesn't even appear to be a DFT by any stretch of the imagination, since a free scalar field on the boundary of AdS is not dual to any known gravitational theory in the bulk.

    It could be that there is some way to make these methods more constructive, or at least make contact with an actual example of gauge-gravity duality. For instance, pure 3d Einstein gravity on AdS with ##G=3L## is potentially dual to the Ising model. There's no SUSY, extra matter, or gauge theory around to complicate things, so maybe a model like this would be more amenable to study.

    With all due respect to an interesting idea, I think the toy model is very far from realistic and doesn't by itself add a great deal of strength to the premise. I would look forward for future work on this, but I wouldn't get caught up in overselling the results so far.
     
  15. Aug 21, 2013 #14
    A few comments about this paper...

    First, although Marolf talks about a dual field theory in the paper, it does not seem to play any role in his actual argument. His actual argument is that the bulk theory satisfies a property that he introduces, which he calls "information holography".

    So I consider the paper to have more in common with the literature which talks about holography but not about holographic duality; for example, work which talks about holographic entropy bounds.

    Second, he appeals to a theorem from axiomatic QFT, the Reeh-Schlieder theorem, in order to argue that his toy model has the property of information holography. I am strongly reminded of the paper from earlier this year, "Why gravity codes renormalization...", which also tried to use a framework from axiomatic QFT.

    Axiomatic QFT, it seems to me, has never caught up with the actual practice of QFT since the Wilsonian revolution of the 1970s - see e.g. this comment by Harvard's Matt Reece. Axiomatic QFT offers a sort of idealized notion of QFT, similar to, say, von Neumann's axiomatization of QM, but real applications of QFT involve a "QFT-like object" with parameters that run under the renormalization group. High-energy physicists have their folk understandings of what this object is and how to calculate with it, but the mathematicians have been very slow to codify the Wilsonian notion of QFT ... for baby steps, see some recent papers by Borcherds, and maybe Kreimer's work on Hopf algebras in renormalization. (The latter may not reach fruition until the current motivic/twistorial/... rethink of theories like super-Yang-Mills, and subsequently, one assumes, theories more like the standard model, has produced an alternative self-sufficient account of what QFT is.)

    So anyway, I have some doubts that the Reeh-Schlieder theorem, which Marolf employs, and which is from the world of axiomatic QFT, applies so readily to the real world of applied QFT. That world of axiomatic QFT, after all, is also the home of Haag's theorem, which is occasionally used to suggest that "applied QFT" has some sort of crisis of legitimacy, because the "QFTs" that it uses, do not exist in the sense of axiomatic QFT. But those QFT-like objects are what is used e.g. by theorists at CERN to understand what the colliders are doing, they obviously work, so the problem must be that axiomatic QFT is talking about the wrong mathematical objects. And so when axiomatic QFT says, via Reeh-Schlieder, that the vacuum is superentangled - and when Marolf goes from that, to arguing that his pseudo-Newtonian theory has "information holography" - I wonder if all that is similarly wrong.

    It's a bit daring to suggest that Marolf is getting his QFT wrong, but if you look at his publication history, he's definitely a relativist rather than a particle physicist. He's written about the renormalization group but also about algebraic QFT [edit: ** this may be wrong, see below **]. He's worked with Ashtekar and Thiemann as well as with Polchinski. He certainly explores in directions where many of his HEP-theorist colleagues would not follow, philosophically - beyond the HEP orthodoxy of string theory and Wilsonian QFT, into the other world of loop variables and algebraic/axiomatic QFT. So his work also has potential significance as another case study for the interminable meta discussion about whether those "other" approaches (to quantum gravity and quantum field theory) can work or not.

    Third, I think the comment by "Lun", in the thread at Woit's that Marcus cites in comment #10, is also of technical interest in evaluating Marolf's paper. (Let me also acknowledge the interest of what fzero has said, though I have nothing to add.)

    Finally, I'll point out that Marolf acknowledges discussions with Aron Wall, who won a thesis prize at GR20 last month. Perhaps someone that damned anti-string heretics will want to follow. ;-)

    ** I may have been wrong here; he had a previous publication about algebraic quantization, not about algebraic QFT.
     
  16. Sep 17, 2013 #15

    marcus

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    Don Marolf has presented his "Holography without Strings" result at Perimeter Institute to a combined session of the String Theory Seminar and Quantum Gravity Seminar. The video of his talk is on PIRSA
    http://pirsa.org/13090060/
     
  17. Sep 18, 2013 #16

    Chronos

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    Pardon my naivety, but, isn't holography focused on boundary conditions like event horizons? It all seems [to me] to be preoccupied with extreme circumstances. Is this the best avenue to a better understanding of the laws of nature, or, could it be diverting attention from more fundamental principles?
     
  18. Sep 18, 2013 #17

    marcus

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    I think you're talking about a gut feeling (which I share) that AdS/CFT and the like have been over-hyped. People can differ as to the way they express this and the REASONS they give. Just at the level of attitude an interesting expression of this was given by Matt Strassler in his report on this month's conference at Stanford. http://profmattstrassler.com/2013/09/16/a-quantum-gravity-cosmology-conference/

    My take on it is that generally speaking I don't think the boundary has to be fraught with "extreme circumstances". It doesn't have to be something as special as the event horizon of a black hole. There may be a certain artificiality about how it's defined (asymptotic flatness...) in some cases but this is not a major difficulty.

    There's valid and interesting math here, but also an intuitive feel of something that's part fad and distraction. I think starting back in 2003 a lot of people gave up on String ever saying anything useful about particle theory, as unification, explaining the Standard Model IOW. And they compensated by focussing on gravity--the "gauge-gravity" duality seen in holographic AdS/CFT context. It was somewhere to go, and a lot of people giving up on the TOE idea needed an exciting new direction. Now the FIREWALL confusion suggests that the "gauge-gravity" hope is unraveling as well. Leonard Susskind has opined that, as currently understood, string appears not to provide a complete picture of quantum gravity.

    So although there are interesting and valid math tools being shown, the AdS/CFT enthusiasm seems to have been disproportionate (perhaps because there was a need for it.)

    That said, I don't want to take away anything from Marolf's result! He finds that string plays no essential role in holography. The observable algebra on the bulk region can be reconstructed from the observables on a region's boundary. No extra dimensions needed. No supersymmetry needed. No stringy stuff.

    The PIRSA talk has rather flakey sound. He was giving the talk from some other location (probably Santa Barbara) and connected by wire to Perimeter. I guess he had to be wearing a headset to listen for questions from the PI audience, and consequently there was feedback. So it is a bit of a job listening to the talk. I found it helpful though,as a supplement to the paper.
     
    Last edited: Sep 19, 2013
  19. Sep 18, 2013 #18

    marcus

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    To recap: Don Marolf recently found that string plays no essential role in holography. In the case of a (general covariant) gravitational field theory, the observable algebra on a bulk region can be reconstructed from the observables on a region's boundary. In Marolf's terminology a dual field theory (DFT), living on the boundary, evolves according to a boundary Hamiltonian and determines what happens in bulk. No extra dimensions, no supersymmetry needed. No stringy stuff.

    Marolf's paper Holography without strings? http://arxiv.org/abs/1308.1977
    His September talk to the combined Quantum Gravity and String seminar at Perimeter Institute:
    http://pirsa.org/13090060/
     
    Last edited: Sep 18, 2013
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