# AdS/CFT w/out Holography and SLOT - Fluctuation Work Theorem

1. Jul 4, 2015

### Jimster41

http://arxiv.org/abs/1507.00591
AdS/CFT without holography: A hidden dimension on the CFT side and implications for black-hole entropy
H. Nikolic
(Submitted on 2 Jul 2015)
We propose a new non-holographic formulation of AdS/CFT correspondence, according to which quantum gravity on AdS and its dual non-gravitational field theory both live in the same number D of dimensions. The field theory, however, appears (D-1)-dimensional because the interactions do not propagate in one of the dimensions. The D-dimensional action for the field theory can be identified with the sum over (D-1)-dimensional actions with all possible values Λ of the UV cutoff, so that the extra hidden dimension can be identified with Λ. Since there are no interactions in the extra dimension, most of the practical results of standard holographic AdS/CFT correspondence transcribe to non-holographic AdS/CFT without any changes. However, the implications on black-hole entropy change significantly. The maximal black-hole entropy now scales with volume, while the Bekenstein-Hawking entropy is interpreted as the minimal possible black-hole entropy. In this way, the non-holographic AdS/CFT correspondence offers a simple resolution of the black-hole information paradox, consistent with a recently proposed gravitational crystal.

The above recent paper, as I understand it, suggests that there is no reason to say that the CFT does not exist in the same number of D as the AdS, as long as information in the +1d (or +nd) does not propagate (or does not freely propagate) in the CFT. This seems like an interesting clarification of the AdS/CFT relationship...

I'm interested in whether or not there is a possible relation between the regulator component $\Lambda$ applied by the AdS free dimension (which does influence the CFT subspace) and the bulk SLOT, which determines the probability of specific Action ala Crooks Fluctuation Theorem, in which time (increasing entropy) and gravity are also connected.

If the regulator is not information free (w/respect to the bulk) but as suggested is just constrained to operate only through the control of re-normalization and not through the CFT action explicitly, is there a natural description of the apparent structure of free energy (why some actions appear to be more probable than others), hence the information emergent in non-equilibrium structure?

p16 "Here h(Λ) is a measure which depends on Λ explicitly, but does not depend on φ(Λ) and g(Λ). The action (49) has the same symmetries as the action (47), but has one dimension more corresponding to Λ. 16 The extra dimension parameterized by Λ is very different from other dimensions parameterized by x µ . As a consequence, the D-dimensional Lorentz group is not a symmetry of (49).

This seems to me to connect the idea of gravity and the intertial mass as a free energy or entropic "force", (ala Verlinde), and likewise to Crooks/Jarsynski Fluctuation Work Theorem

http://arxiv.org/abs/1001.0785
On the Origin of Gravity and the Laws of Newton
Erik P. Verlinde
(Submitted on 6 Jan 2010)
Starting from first principles and general assumptions Newton's law of gravitation is shown to arise naturally and unavoidably in a theory in which space is emergent through a holographic scenario. Gravity is explained as an entropic force caused by changes in the information associated with the positions of material bodies. A relativistic generalization of the presented arguments directly leads to the Einstein equations. When space is emergent even Newton's law of inertia needs to be explained. The equivalence principle leads us to conclude that it is actually this law of inertia whose origin is entropic.

http://arxiv.org/abs/0809.0025
The length of time's arrow
Edward H. Feng, Gavin E. Crooks
(Submitted on 29 Aug 2008)
An unresolved problem in physics is how the thermodynamic arrow of time arises from an underlying time reversible dynamics. We contribute to this issue by developing a measure of time-symmetry breaking, and by using the work fluctuation relations, we determine the time asymmetry of recent single molecule RNA unfolding experiments. We define time asymmetry as the Jensen-Shannon divergence between trajectory probability distributions of an experiment and its time-reversed conjugate. Among other interesting properties, the length of time's arrow bounds the average dissipation and determines the difficulty of accurately estimating free energy differences in nonequilibrium experiments.

http://arxiv.org/abs/cond-mat/9901352
The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
Gavin E. Crooks
(Submitted on 29 Jan 1999 (v1), last revised 29 Jul 1999 (this version, v4))
There are only a very few known relations in statistical dynamics that are valid for systems driven arbitrarily far-from-equilibrium. One of these is the fluctuation theorem, which places conditions on the entropy production probability distribution of nonequilibrium systems. Another recently discovered far-from-equilibrium expression relates nonequilibrium measurements of the work done on a system to equilibrium free energy differences. In this paper, we derive a generalized version of the fluctuation theorem for stochastic, microscopically reversible dynamics. Invoking this generalized theorem provides a succinct proof of the nonequilibrium work relation.

Last edited: Jul 4, 2015
2. Jul 4, 2015

### mitchell porter

I am not going to try to understand what you are talking about. But that first paper is ridiculous. It describes a relatively trivial dimensional truncation that has nothing to do with the real AdS/CFT. It's as if someone were to write a paper about a "non-multiplicative product" which is defined by adding two numbers rather than multiplying them, and then went on to solemnly say that this has major implications for the times table.

3. Jul 5, 2015

### Jimster41

I appreciate the heads up on the first paper. I thought I was following it... but. I don't suppose you could say a bit more about how it's argument breaks down, where the formalism is too thin or wrong. It did seem a somewhat outrageous proposal.

4. Jul 5, 2015

### ShayanJ

I think its better to let the author explain himself.(@Demystifier)

5. Jul 5, 2015

### Jimster41

Not my intention to put him on the spot here. I thought it was an interesting and accessible paper, and was excited by it. I'll admit I had seen a different paper of his, and had a similar experience, before I knew that it was him. Which is why I read (tried) this one.

At a minimum this one helped clarify for me the question of what AdS/CFT correspondence is and what it might indicate.

I looked up his inspire profile. (What a crazy crazy notion that whole thing is, but I guess it makes sense in academia) His does not scream "crackpot" to say the least. So I think a critique kindof needs to be specific.

Last edited: Jul 5, 2015
6. Jul 5, 2015

### mitchell porter

I am sleep-deprived right now, so this is not a proper critique, but I will say a bit more. AdS/CFT relates gravity in N dimensions to a gauge theory in N-1 dimensions. The author wants the gauge theory to be N-dimensional too, so he adds an extra dimension on the gauge theory side of the correspondence and says, the fields extend into that extra direction but what happens there doesn't affect what happens in the (N-1)-dimensional slice that we started with. That's even in the abstract.

From the paper I now see that the motivation is to defend the author's model of a quantum black hole as a "gravitational crystal". Apparently it contradicts the usual black-hole thermodynamics in which the entropy is proportional to the area of the event horizon. Instead he has it as proportional to the volume. AdS/CFT agrees with the standard view, and that's why he wants to add a dimension to the CFT.

I missed some of this when I first skimmed the paper. In particular, not knowing the motivation made it seem like nonsense - why would anyone add a dimension, in a way designed to affect nothing, and then claim that it does? That's why I was so scornful.

Now I would say, OK, I see the motive, but there's still no way this makes sense! And in fact, now I see that the author's quarrel is not just with AdS/CFT, but even with the semiclassical picture due to Bekenstein and Hawking.

So there definitely ought to be grounds for specific critique. But I won't be figuring out those details tonight.

7. Jul 5, 2015

### Jimster41

All of that is consistent with what I got. I thought the idea was that the gauge theory was D dimensional, but not in the action; last paragraph section 4.2. Then through section 5 he is saying there is a degree of freedom associated with the extra hidden dimension and associated that with the "Unparticle" and the UV cutoff in the CFT. This is the part where it gets very (especially) fuzzy for me.

It's only my intuition, but what I wanted to do (my question such as it is) is how might that proposed extra "hidden" DOF (w/respect to the action) relate to non-local Superselection Rules, and or the distribution of critical points in the renormalization flow? They just both come to mind.

The thing I keep thinking today (trying to get a little more clear) is can the decrease of the energy density of the universe, the general increase of entropy, and the local (gravitationally induced) increase in order or negentropy (emergent structure) be seen through this onion scheme as one process, where information in one dimension acts very differently than information in the other dimensions in the D dimensional space. Where maybe something akin to Smolin's latest notion of Variety and his p-Adic like metric, rules the hidden dimension, affecting the D-1 fields and action only indirectly.

Could the fluctuation work theorem be imagined as work done by that extra DOF, giving in some sense a very different explanation for what is and isn't more probable in the action, in fluctuation, an explanation of why (more how) we have both increasing overall entropy and locally increasing order?

Thanks for saying more by the way.

Last edited: Jul 5, 2015
8. Jul 6, 2015

### Demystifier

I am always open to specific critique based on thought-out arguments.

I have no intention to repeat here all the arguments that I have written in the paper, but it can be useful to emphasize here some crucial ideas that otherwise might be missed by a casual reader.

For the moment let me emphasize only one crucial idea. Just because the two theories are related (one in D dimensions and another in D-1 dimensions) does not immediately mean that the two theories are fully equivalent. In AdS/CFT literature, the difference between "being related" and "being equivalent" is often not clearly stated. One of my points is to make this difference clear and to stress that most of the evidence for AdS/CFT is evidence for the relation (correspondence), not an evidence for the equivalence (duality). This should be particularly clear in Sec. 3.

Last edited: Jul 6, 2015
9. Jul 6, 2015

### Demystifier

In the last paragraph of Sec. 4.2 it should be clear that all D dimensions (in this case D=4) are in the action.
The purpose of this section is to give a simple example of a general mechanism of hiding one dimension in the onion structure. This section is not really about AdS/CFT.

10. Jul 6, 2015

### Demystifier

May I know which paper was that?

11. Jul 6, 2015

### Demystifier

Unparticle here is only for an analogy, because unparticle is a simple example of a theory with an onion structure. The AdS/CFT duality itself does not involve unparticles.

Note also that UV cutoff is related to the extra dimension even in the standard holographic AdS/CFT. Namely, the cutoff in CFT is "dual" to the coordinate z on AdS. The standard holographic interpretation of this, however, is that z somehow must be a "fake" dimension in AdS because the cutoff is not a dimension in CFT. My non-holographic interpretation is the opposite: the cutoff must be a genuine dimension in CFT because there is nothing "fake" about the coordinate z in AdS.

It all boils down to the choice which theory is much weirder than it looks at first sight. The standard holographic interpretation is that the theory on AdS is weird, because it really has a smaller number of dimensions than it looks at first. The alternative non-holographic interpretation is that the CFT theory is weird because it has a larger number of dimensions than it looks at first. In each case, one theory looks weird and another looks normal.

Of course, it can be very non-intuitive that a cutoff can be a dimension. But it is probably equally non-intuitive that mass can be a dimension. And yet, in the unparticle subsection, I have proved in a very straightforward way how can mass be a dimension. Equipped with this insight one can develop a new intuitive way of thinking about dimensions (do you remember how non-intuitive was to you when you heard for the first time that in relativity time is a dimension?), which should help to grasp more easily how cutoff can be a dimension.

12. Jul 6, 2015

### Demystifier

Did the standard AdS/CFT proposal looked outrageous the first time you heard about that?

13. Jul 6, 2015

### Demystifier

Does it mean that you are not in academia?

Last edited: Jul 6, 2015
14. Jul 6, 2015

### Demystifier

I can understand that it doesn't seem to make sense at first. But then with standard semiclassical picture, and even with standard AdS/CFT, there is the black-hole information paradox. So the standard picture also "does not make sense" at a certain level. So if the alternative to one idea which "makes no sense" is another idea which also "makes no sense", then perhaps one of them should make sense after more scrutiny.

15. Jul 6, 2015

### Jimster41

I was being sympathetic to Mitchell Porter's general reaction. I typed "bold" first but that seemed too biased toward agreement.

No I'm not in academia. Just a fan. I've been reading about cosmology and science of all kinds every since I gave up on the problem of Theodicy and dropped out of seminary. Now I'm an engineer. Actually, I kindof like to think I never really gave up.

Your post 11 clarifies and highlights what I found interesting about the paper. Have you seen that paper by Smolin? I keep thinking it somehow offers a weird model of that special type of influence on the action. I ran into p-Adic numbers recently. Fascinating. I wish I understood them. They also seem potentially relevant, I don't know why.

Last edited: Jul 6, 2015
16. Jul 6, 2015

### Demystifier

No I did not. Can you give the link?

17. Jul 6, 2015

### Jimster41

http://arxiv.org/abs/1506.02938

the part which came to mind in trying to understand the action you are describing is the idea that non-locality (or maybe "alt-locality") is because the metric is not same for some dimensions of the overall space as it is for others. This would lead to potentially interesting interaction, and mysteries in the behavior of the action when viewed only through the lens of one metric (our CFT view).

Which, on my third+ time through is like what I take your proposal with respect to Lambda and z to mean.

Here's a link to the wiki on p-adic. Which I find immediately impenetrable, but tantalizing, in the way it sounds like what Smolin is suggesting.

when I say "alt-locality" I am thinking of your statement above, that the hidden dimension in the AdS is real, it contains information, has rules, a metric, and does things to the CFT.

Last edited: Jul 6, 2015
18. Jul 7, 2015

### mitchell porter

OK, Mr Demystifier, I managed to peel a few layers from my own "onion of misinterpretations" of your paper, and I think I have the basics now. You're actually rewriting the usual CFT action, as an integral over scales (equation 49), in a way resembling the rewrite of the unparticle action as an integral over masses (equation 43); and the scale parameter is your hidden dimension.

I still haven't figured out how to think about these claims, but I do have two initial doubts about whether the theory described really does behave like it has D dimensions rather than D-1.

First, can you obtain a meaningful algebra of quantum field operators from this action, that are indexed by all D coordinates including Λ, i.e. an algebra of local field operators of the form φ(x,Λ) in which x and Λ vary independently, or will it always be the case that in practice, you only get φ(x)'s?

Second, are you sure that the entropy in this theory does actually scale like a standard D-dimensional theory?

19. Jul 7, 2015

### Demystifier

That's almost correct, but to avoid misinterpretation let me clarify a few things. In renormalization theory, the scale is not the same thing as the cutoff. In principle, the scale can be changed even with a fixed cutoff. Renormalization group (RG) is a useful tool, but physics can be done even without RG. As long as one does not use RG, in the usual CFT action the cutoff is treated as a fixed quantity. Thus it is important to emphasize that (43) is an integral over cutoffs, not over scales. In this sense, I do not rewrite the usual action, but collect all the possible usual actions (corresponding to different fixed cutoffs) into one big action. That's not something that you do in usual CFT. The big action has much more degrees of freedom than the usual CFT action.

The answer depends on what exactly do you mean by "field algebra". If you mean the canonical commutation relations between fields and their conjugate momenta, then it's φ(x,Λ) in which x and Λ vary independently. If you mean the algebra of symmetries of the action, then its essentially φ(x). My D-dimensional action only has the symmetries of the standard D-1 dimensional action.

If you are still confused, let me say that it is somewhat similar to generations in the standard model of particle physics. If we neglect the mixing between different generations in the weak sector, the 3 generations of the standard model can be viewed as 3 layers of an onion. Each generation has the same symmetries, but different masses. The 3 generations do not have more symmetry than one generation, but 3 generations have more entropy than one generation. In analogy with 3 generations of the standard model, my theory can be thought of as a theory with an infinite number of "generations" of CFT fields.

Yes. The entropy scales with the number of degrees of freedom, not with the number of symmetries of the action. The number of degrees of freedom corresponds to the number of conjugate pairs of fields and their conjugate momenta.

Last edited: Jul 7, 2015
20. Jul 7, 2015

### Jimster41

I probably am not picturing this right. Is there a precedent for describing an action like 49, where a term is part of the gauge theory action, but has a discrete/intermittent/periodic participation or effect? I'm confused about the implications of the paragraphs down to eq52.

My understanding is that cuttoffs are essential in enabling the Re-normalization Group to describe the fields and particles of the Standard Model. They (cuttoffs) are the cause of the discrete scale in-variance of the gauge theory. And there is some debate as to whether or not they are real or just tools to allow integrals of the gauge field theory to be calculated in a way that matches experiment.

Is eq52 just saying that the role of the hidden dimension is to parameterize the structure of the guage theory symmetries as a function of scale?

Is it wildly incorrect to say that it is parameterizing the Hamiltonian of the gauge theory - as a function of scale?

Last edited: Jul 7, 2015