Is loop quantum gravity dual to CFT?

[kodama]

TL;DR Summary

bulk theories of quantum gravity are dual to each other

this paper
arXiv:2310.02958 [pdf, other]
What if Quantum Gravity is "just'' Quantum Information Theory?
Aron C. Wall
Comments: 6 pages, 2 figures. Additional references added to arxiv version
Journal-ref: Proc. 28th Solvay Conf. Phys., ed. D. Gross, A. Sevrin, P. Zoller, World Scientific Publishing Co., Singapore, 2023
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)

I suggest the possibility that holographic quantum gravity is, in some sense, equivalent to quantum information theory. Some radical implications would follow. First, the theory of quantum gravity should have no adjustable coupling constants, similar to string theory. Thus, all complete bulk theories of quantum gravity are dual to each other. By setting up an appropriately entangled state, it should be possible to find wormholes connecting any two quantum gravity theories (e.g. string theory and loop quantum gravity). Secondly, if we represent space at one time as a tensor network, then dynamics is automatically encoded via gauge-equivalent descriptions of the boundary state. This would appear to imply, contrary to semiclassical expectations, that a closed universe should have only one state.

except

would quantize a LQG model in AdS. via holographybe dual to N = 4 Super Yang-Mills and also string theory

 

[Demystifier]

String theorists compete who will propose a weirder duality. Extra credit is deserved if your evidence for the duality is so deep that you don't need any equations. Obvious evidence against duality is not welcome, but a complicated equation-free argument against duality, that itself has deep weird implications, may attract some attention.

 

[kodama]

String theorists compete who will propose a weirder duality. Extra credit is deserved if your evidence for the duality is so deep that you don't need any equations. Obvious evidence against duality is not welcome, but a complicated equation-free argument against duality, that itself has deep weird implications, may attract some attention.

would LQG in 5D AdS. via holography also be dual to N = 4 Super Yang-Mills ?

 

[Demystifier]

would LQG in 5D AdS. via holography also be dual to N = 4 Super Yang-Mills ?

You didn't understand my point, did you?

 

[mitchell porter]

This "paper" actually says nothing about loop quantum gravity. The author is apparently just musing, what if quantum gravity in all its forms is dual to entangled qubits? He then concludes that all possible worlds of quantum gravity could be connected by wormholes, since to make a wormhole between two worlds, you would just need to entangle dual qubits from the two worlds.

In order to illustrate his point, he says, let's suppose string theory and loop quantum gravity are two such worlds, then we could have a wormhole between them! But this is quite hypothetical and he presents no idea for how qubit holography would work in loop quantum gravity. He could equally have said, if the Land of Oz has a qubit dual, then there could be a wormhole from string theory to the Land of Oz, and it would have had just as much physics content.

This paper belongs to a genre we could call "qubitzer quantum gravity". Qubitzer is a word that Leonard Susskind introduced, to refer to people who approach quantum gravity via quantum information theory. An anonymous young string theorist ("String King") has recently been tweeting that the rise of qubitzers represents a severe lowering of standards in quantum gravity. I suppose the qubitzers would defend themselves by saying that making simplified models is a common thing in physics, and that's all they're doing.

 

[kodama]

the reason I posted this essay is that
the AdS/CFT correspondence states that type IIB string theory on the product space A d S 5 × S 5 is equivalent to N = 4 supersymmetric Yang–Mills theory on the four-dimensional boundary

and Aaron Wall also suggests that LQG in AdS space is also equivalent to A d S 5 × S 5 is equivalent to N = 4 supersymmetric Yang–Mills theory on the four-dimensional boundaryif both theories are equivalent to the same N = 4 supersymmetric Yang–Mills theory on the four-dimensional boundary, aren't they equivalent to one another, with his explanation involving quantum information theory and wormholes

type IIB string theory on the product space A d S 5 × S 5 is equivalent to LQG in product space A d S 5 × S 5

 

[Demystifier]

let's suppose string theory and loop quantum gravity are two such worlds, then we could have a wormhole between them

I don't even know what that means. String theory and loop quantum gravity are not two physical objects, they are two formalisms. What does it mean to have a wormhole (which is a physical object), between two formalisms? This is like saying that we can have a tube connecting Heisenberg and Schrodinger picture of quantum mechanics. To me, it sounds like postmodern nonsense. Is there a way to explain the idea with more precise words?

 

[mitchell porter]

Is there a way to explain the idea with more precise words?

As you would know, the Schwarzschild solution of general relativity, which describes a static black hole, can be extended so that it is actually a wormhole connecting two space-times. Maldacena 2001 proposed that the AdS counterpart of this (i.e. black hole in AdS, inwardly extended so as to become a wormhole to a second AdS space-time) is described by the tensor product of two CFTs, one for each AdS space-time. To be more precise, a state in the Hilbert space Hilb_CFT1 x Hilb_CFT2 should be capable of describing such a geometry. This is the root from which ER=EPR, wormholes in quantum computers, and so on, ultimately derives.

It is a popular idea that every theory of quantum gravity in AdS should have a CFT dual. So Aron Wall is saying, if LQG (for example) is well-defined in AdS, not only should it have a CFT dual, but it should be possible to carry out the construction above, with CFT1 dual to string theory in AdS, and CFT2 dual to LQG in AdS, describing a wormhole with string theory on one end, and loop quantum gravity on the other end. He remarks that this would imply that string theory and loop quantum gravity are just different phases of a single unique theory of quantum gravity.

For now this is hypothetical, since there is no standard LQG description of AdS quantum gravity. After discussion in another thread, I have tentatively concluded that the right way to think of quantum gravity in Ashtekar variables, is just as a change of variables from quantum gravity based on a metric (this change of variables was carried out by some Russian physicists, as reported in that thread), and that either way it's probably UV-incomplete. If you think string theory is the right way to UV-complete quantum gravity, the Ashtekar variables might offer a new perspective on string theory. Since Ashtekar gravity isn't based on a metric, maybe it's related somehow to topological string theory, which is string theory minus the metric, more or less. But as far as I know, that's just speculation.

 

[kodama]

For now this is hypothetical, since there is no standard LQG description of AdS quantum gravity.

does the Kodama states qualify as standard LQG description of AdS quantum gravity?

 

[mitchell porter]

does the Kodama states qualify as standard LQG description of AdS quantum gravity?

Maybe one can say it is the proposed LQG description of quantum gravity in De Sitter space. I'm basing my judgement on some papers cited in the Wikipedia article on the Kodama state: Smolin 2002, Witten 2003, and Randono 2006a, 2006b. Smolin promotes the Kodama state as appropriate for De Sitter space, Witten argues that half the resulting particle states will be unviable (negative energy and probabilities undefined), Randono proposes that the states can be modified and rescued. At the end of his second paper, Randono says he doesn't know if the states he defines manage to avoid negative energies.

In Witten's paper, page 2, there is a section called "Upside Down Wave Function Of The Harmonic Oscillator". He's describing a simple analogy of the Kodama state. He starts with the usual ground state of a quantum harmonic oscillator, which is a gaussian (i.e. a Bell curve). A gaussian has the form exp(-x^2). The "upside down" wavefunction has the form exp(+x^2), which is a U-shaped curve that increases exponentially towards +∞ and towards -∞. This shape is the source of the problems; but it's also because the cosmological constant, which appears in the exponent, is positive. For a negative cosmological constant, such as for Anti De Sitter space, it seems like you should get a normal gaussian wavefunction, for which probabilities are well-defined. But I didn't see any discussion of this in any of these papers, since they were focused on the De Sitter case.

There is a 2022 paper by Stephon Alexander et al which cites some later works, that keep tinkering with the Kodama state. For example, gravitons come in two polarizations, and one problem with the Kodama state is that one polarization will be positive energy, the other will be negative energy (this is in Witten 2003). But maybe you can just do without one of those polarizations. Just today, Peter Woit has released such a proposal ("Spacetime is Right-handed"). He doesn't mention it, but it would be logical to regard a Kodama state as a candidate for the wavefunction of the universe in his theory.

Another detail, that may appeal to @Demystifier (who I believe has written about Bohmian mechanics), is that the Kodama state can be interpreted as a quantum Hamilton-Jacobi state. The phase is the Chern-Simons invariant that is used to construct the state, and the gradient of the phase gives rise to "self-dual" solutions that would be the Bohmian trajectories. (This is in section 4 of Smolin 2002, but without any reference to Bohm, and indeed Bohmian gauge theory and Bohmian quantum gravity have the problem that they need to be gauge-fixed before you can define trajectories, which contradicts the usual attitude towards symmetry in physics.)

 

[kodama]

For a negative cosmological constant, such as for Anti De Sitter space, it seems like you should get a normal gaussian wavefunction, for which probabilities are well-defined. But I didn't see any discussion of this in any of these papers, since they were focused on the De Sitter case.

any chance you could write a paper on this ? i.e Kodama and 4d Anti De Sitter space

what CFT is duality with 4d Anti De Sitter space?

. Just today, Peter Woit has released such a proposal ("Spacetime is Right-handed"). He doesn't mention it, but it would be logical to regard a Kodama state as a candidate for the wavefunction of the universe in his theory.

perhaps could you comment on his blog

Another detail, that may appeal to @Demystifier (who I believe has written about Bohmian mechanics), is that the Kodama state can be interpreted as a quantum Hamilton-Jacobi state. The phase is the Chern-Simons invariant that is used to construct the state, and the gradient of the phase gives rise to "self-dual" solutions that would be the Bohmian trajectories. (This is in section 4 of Smolin 2002, but without any reference to Bohm, and indeed Bohmian gauge theory and Bohmian quantum gravity have the problem that they need to be gauge-fixed before you can define trajectories, which contradicts the usual attitude towards symmetry in physics.)

very interesting

 

[mitchell porter]

In a thread about using Ashtekar variables in quantum gravity, we talked about a Bohmian interpretation of the Kodama state.

Two weeks later, a paper using Ashtekar variables in quantum gravity, talks about a Bohmian interpretation of the Kodama state:

"A Realist Interpretation of Unitarity in Quantum Gravity"

What a coincidence!

 

[kodama]

In a thread about using Ashtekar variables in quantum gravity, we talked about a Bohmian interpretation of the Kodama state.

Two weeks later, a paper using Ashtekar variables in quantum gravity, talks about a Bohmian interpretation of the Kodama state:

"A Realist Interpretation of Unitarity in Quantum Gravity"

What a coincidence!

what are your thoughts on the Bohmian interpretation of the Kodama state

 

[kodama]

any opinions of

https://arxiv.org/abs/2310.19729
https://arxiv.org/abs/2310.19722