What if unification does not work?

  • #1
Randy Subers
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TL;DR Summary
Looking for papers for alternatives to current unification efforts
I will try to word this in a way that does not violate forum rules.
As I look at the struggles of string theory and loop quantum gravity and the struggles of trying to unify quantum mechanics and general realtivity in general such as the need for a framework for quantum physics which does not exist in GR and this leading to infinities in values this leads me to wonder what if they will not unify at least in the way we currently visualize them unifying (such as a quantum version of GR). My question is whether there have been any papers published on what if unification as we currently visualize it cannot be done and a new approach (not just a new theory) is needed.
 
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  • #2
Randy Subers said:
TL;DR Summary: Looking for papers for alternatives to current unification efforts

I will try to word this in a way that does not violate forum rules.
As I look at the struggles of string theory and loop quantum gravity and the struggles of trying to unify quantum mechanics and general realtivity in general such as the need for a framework for quantum physics which does not exist in GR and this leading to infinities in values this leads me to wonder what if they will not unify at least in the way we currently visualize them unifying (such as a quantum version of GR). My question is whether there have been any papers published on what if unification as we currently visualize it cannot be done and a new approach (not just a new theory) is needed.
There seem to be two different kinds of unification you are referring to:
1. TOEs. Theories that unify gravity with the EM, weak, and strong nuclear forces.

2. Quantum Gravity. A "unification" of GR and QM.

We have some reason to believe that there is a TOE, but it is not necessary. (It would be really nice, though, which is why a lot of time has been spent researching it.)

Quantum Gravity, though, has to exist. We need some kind of Quantum version of gravity to explain what gravity does on the Quantum level. Now, whether we already know enough Physics and Math to build such a theory is an open question. But there has to be one.

Which unification are you asking about?

-Dan
 
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  • #3
topsquark said:
There seem to be two different kinds of unification you are referring to:
1. TOEs. Theories that unify gravity with the EM, weak, and strong nuclear forces.

2. Quantum Gravity. A "unification" of GR and QM.

We have some reason to believe that there is a TOE, but it is not necessary. (It would be really nice, though, which is why a lot of time has been spent researching it.)

Quantum Gravity, though, has to exist. We need some kind of Quantum version of gravity to explain what gravity does on the Quantum level. Now, whether we already know enough Physics and Math to build such a theory is an open question. But there has to be one.

Which unification are you asking about?

-Dan
I am talking about unification of GR and QM. While the universe obviously knows what to do in the case of extreme conditions such as near the center of a black hole, it is not obvious to me that the current mathmatical frameworks (such string theory and LCG) are even taking the correct approach (they may be dead ends) and an entirely new type of approach may be needed. I am hoping someone with much better knowledge than I do has looked at this possibility and published something on it, hopefully with some possible mathematical concepts to go with it.
 
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  • #4
Randy Subers said:
I am talking about unification of GR and QM. While the universe obviously knows what to do in the case of extreme conditions such as near the center of a black hole, it is not obvious to me that the current mathmatical frameworks (such string theory and LCG) are even taking the correct approach (they may be dead ends) and an entirely new type of approach may be needed. I am hoping someone with much better knowledge than I do has looked at this possibility and published something on it, hopefully with some possible mathematical concepts to go with it.
There are always lots of people out there working on alternative theories. Keep an eye on the gr-qc archive and you should see a steady supply.

It's a little unusual to object to string theory on the grounds that it's not good as a theory of quantum gravity. The most common objection to string theory is that it posits too many things that we don't see, especially in the world of particles. The next most common objection is that it doesn't explain what we do see, it just offers us a zillion possible geometries to search through.

But there's not much we can see or test in quantum gravity, so one might have preferred string theory there, as a source of numerous models that are at least full of calculable properties, and therefore capable of being studied logically. People who disfavor string theory in this area usually already have some other specific technical idea in mind.

Of course, in the absence of definitive proof, it makes sense to explore all possibilities. This can even help the "mainstream" approaches, by addressing questions of the field in a fresh or complementary way... As I said, the world is full of alternative theories, such as Penrose's twistor theory, the theories of semi-outsiders like Weinstein, Woit, and Wolfram, and any number of academics you've never heard of, laboring away in universities around the world, on personal theories that only their colleagues know about. There was a conference in Vancouver earlier this year, you might want to view their video archive.

Is there a particular perspective on quantum gravity that is motivating you?
 
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  • #5
mitchell porter said:
There are always lots of people out there working on alternative theories. Keep an eye on the gr-qc archive and you should see a steady supply.

It's a little unusual to object to string theory on the grounds that it's not good as a theory of quantum gravity.
does string theory reproduce all GR including

Screenshot 2023-08-19 at 22-33-59 Smolin-TroubleWithPhysics.pdf.png
Screenshot 2023-08-19 at 22-34-15 Smolin-TroubleWithPhysics.pdf.png
 
  • #6
kodama said:
does string theory reproduce all GR including [time-varying backgrounds -MP]
This is an excellent point. There is very little work within string theory on time-varying backgrounds. Even the debate over the status of De Sitter space in string theory, is an example of this.

I think this is mostly because people just haven't figured out how to represent a generic time-varying background in string theory. String theory is most thoroughly understood in the context of spaces where the "structure at spatial infinity" stays the same. So two huge problem areas are (1) time-varying backgrounds (2) compact space-times.

In this regard, Witten's very latest paper is interesting, because rather than talk about the asymptotic behavior of strings when they are far apart (the basis of the S-matrix approach to particle physics), he bases everything on what an observer following a particular world-line encounters.
 
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  • #7
Arguing that quantum space-time is necessary is this 2021 paper, while an example of paper seeking to do quantum physics in a classical space-time can be found in 2012 and one can also consider a discussion of the 2019 paper that tries to merge GR and quantum mechanics without a true quantum gravity.

In my view, the necessity of quantum gravity does not seem to be rigorously established, at least not in a manner that can command consensus support among scientists in the relevant fields.
 
  • #8
mitchell porter said:
This is an excellent point. There is very little work within string theory on time-varying backgrounds. Even the debate over the status of De Sitter space in string theory, is an example of this.

I think this is mostly because people just haven't figured out how to represent a generic time-varying background in string theory. String theory is most thoroughly understood in the context of spaces where the "structure at spatial infinity" stays the same. So two huge problem areas are (1) time-varying backgrounds (2) compact space-times.

In this regard, Witten's very latest paper is interesting, because rather than talk about the asymptotic behavior of strings when they are far apart (the basis of the S-matrix approach to particle physics), he bases everything on what an observer following a particular world-line encounters.
string theory apparent inability inconsistency with deSitter spacetime, and time varying background rule it out as a theory of QG?
 
  • #9
kodama said:
string theory apparent inability inconsistency with deSitter spacetime, and time varying background rule it out as a theory of QG?
De Sitter space may be a problem for quantum gravity in general, not just string theory. There are many papers arguing that fields in De Sitter space, including the gravitational field, develop quantum mechanical instabilities (e.g. through massive particle production) that force a change in the geometry. Some authors compared it to black hole evaporation: classically a black hole geometry is eternal, but quantum mechanically you have Hawking radiation, and the event horizon decays to nothing.

The situation in string theory is that many alleged De Sitter vacua have been constructed, but they are all really approximations, and the question is whether some neglected effect left out of the approximation invalidates it. Also, empirically, we do not actually know that we are living in De Sitter space. If "dark energy" is vacuum energy, then yes we are, but it could be e.g. a "quintessence" quantum field. Cumrun Vafa, who is probably the most prominent "De Sitter denier" in string theory right now, has been making stringy models of quintessence. (Actually I think the aspect of this that is most uncomfortable for mainstream physicists, is that instability of De Sitter space poses problems for inflation too.)

As for the general problem of time-varying backgrounds in string theory, others have been investigated with varying degrees of rigor. It would be cool if the real world was an example of Hellerman-Swanson... There are many things that could be related in various ways. Maybe the instability of De Sitter and the criticality of our Higgs vacuum are related. Maybe MOND is due to a quantum correction arising from the De Sitter instability. But that's getting off topic. :-)
 
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  • #10
mitchell porter said:
De Sitter space may be a problem for quantum gravity in general, not just string theory. There are many papers arguing that fields in De Sitter space, including the gravitational field, develop quantum mechanical instabilities (e.g. through massive particle production) that force a change in the geometry. Some authors compared it to black hole evaporation: classically a black hole geometry is eternal, but quantum mechanically you have Hawking radiation, and the event horizon decays to nothing.

The situation in string theory is that many alleged De Sitter vacua have been constructed, but they are all really approximations, and the question is whether some neglected effect left out of the approximation invalidates it. Also, empirically, we do not actually know that we are living in De Sitter space. If "dark energy" is vacuum energy, then yes we are, but it could be e.g. a "quintessence" quantum field. Cumrun Vafa, who is probably the most prominent "De Sitter denier" in string theory right now, has been making stringy models of quintessence. (Actually I think the aspect of this that is most uncomfortable for mainstream physicists, is that instability of De Sitter space poses problems for inflation too.)

As for the general problem of time-varying backgrounds in string theory, others have been investigated with varying degrees of rigor. It would be cool if the real world was an example of Hellerman-Swanson... There are many things that could be related in various ways. Maybe the instability of De Sitter and the criticality of our Higgs vacuum are related. Maybe MOND is due to a quantum correction arising from the De Sitter instability. But that's getting off topic. :-)

Loop quantum gravity Kodama state describes de Sitter space, may not be physical though.

Do you know if LQG Spinfoam or other QG can correctly handle time varying backgrounds?

So how is DeSitter related to MOND? this thread is about unification
 
  • #11
kodama said:
So how is DeSitter related to MOND? this thread is about unification
According to MOND, a novel modification to Newtonian gravity comes into play at very small accelerations, below a_0. In "natural units", the associated length scale, c^2 / a_0, is approximately the De Sitter radius of our universe (if it is De Sitter space). This could just be a coincidence, but MOND theorists have speculated that it is a clue to the mechanism. For example, Mordehai Milgrom, the originator of MOND, writes at Scholarpedia:

"if in some way, yet to be established [references omitted] ... , a body of acceleration a is probing distances ∼ ℓ_a, then a body with a ≫ a_0 does not probe the nontrivial (curved) geometry of the Universe, while a body with a ≪ a_0 does."

In other words, one supposes that there is an extremely long-distance or nonlocal contribution to gravity, and that dynamics changes for accelerations below a_0 because the De Sitter cosmological horizon is an absolute limit to how far this nonlocal contribution can stretch.

There might be other ways to do it, e.g. virtual particles coming from the De Sitter horizon. Tom Banks had a model where virtual gravitinos from the De Sitter horizon indirectly break supersymmetry. His student Lubos Motl had an idea for "Holographic Newtonian Dynamics" (HOND) that was to obtain MOND by a cutoff associated with the presence of the cosmological horizon - I don't remember the details.
kodama said:
Do you know if LQG Spinfoam or other QG can correctly handle time varying backgrounds?
I would think that you could consistently do basic perturbative quantum gravity (i.e. simple Feynman diagrams with a small number of gravitons) in a lot of time-varying backgrounds, so long as gravity didn't get too strong. The reasoning is that if the quantum effects are small enough, you can model the whole thing as a time-varying classical background with small quantum perturbations on top of that.

But problems would unavoidably set in once you dealt with strong curvature and/or multi-graviton interactions. Then you have to deal with quantum superpositions of geometry, and the non-renormalizability of perturbative quantum gravity, and you're back facing the hard problems of quantum gravity.

If someone demanded that I pick one fundamental framework in which to tackle time-varying backgrounds, I might suggest the timeless twistor holography of Yasha Neiman, where the time-variation is holographically dual to some timeless initial or final boundary condition, and you study it using twistor variables because everything is better with twistors. And then maybe think about applying it to spacelike branes (S-branes) from string theory. But it's just something to work on, I certainly don't know if it's the right approach.
kodama said:
Loop quantum gravity Kodama state describes de Sitter space, may not be physical though.
As you know, my attitude is that I believe the Ashtekar variables to be meaningful, but at least some of the classic LQG approaches to be wrong. If I was trying to make the Kodama state work, maybe I'd try throwing together Alexander et al 2022, Wieland 2023, and Neiman 2023. The last two papers are only about the "self-dual" sector of gravity, so they would also need to be extended.
 
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  • #12
mitchell porter said:
As you know, my attitude is that I believe the Ashtekar variables to be meaningful, but at least some of the classic LQG approaches to be wrong. I
what do you think is a better way to turn Ashtekar variables into a quantum gravity?
 
  • #13
mitchell porter said:
As you know, my attitude is that I believe the Ashtekar variables to be meaningful, but at least some of the classic LQG approaches to be wrong. If I was trying to make the Kodama state work, maybe I'd try throwing together Alexander et al 2022, Wieland 2023, and Neiman 2023. The last two papers are only about the "self-dual" sector of gravity, so they would also need to be extended.
what do you think of "self-dual" sector of gravity
 
  • #15
mitchell porter said:
In this regard, Witten's very latest paper is interesting, because rather than talk about the asymptotic behavior of strings when they are far apart (the basis of the S-matrix approach to particle physics), he bases everything on what an observer following a particular world-line encounters.
That paper definitely addresses some of the key issues IMO. Witten explicitly acknowleddges that the problem with current theory is that applies to external observers. This is a key issue I think, and we can not avoid facing it at some point. And of course, there is no such thing as all real obsevers are inside the one universe.

I wil read the details more carefully later.

/Fredrik
 
  • #17
kodama said:
why don't you write a paper
If I actually assemble these ingredients into something worthwhile, maybe I will. There's another possible ingredient by the way, that maybe Ashtekar gravity would arise from string theory via ambitwistor strings.
kodama said:
what do you think about joining the weak force to Ashketar variables?
We've discussed this before... It would be interesting if you got both SU(2)s from an SO(4), but why would the SU(2)s behave so differently? Maybe they both start complex, and one is reduced to real SU(2) for some reason and becomes the weak gauge field, and the other one stays complex and becomes Ashtekar gravity somehow.
 
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  • #18
mitchell porter said:
If I actually assemble these ingredients into something worthwhile, maybe I will. There's another possible ingredient by the way, that maybe Ashtekar gravity would arise from string theory via ambitwistor strings.

We've discussed this before... It would be interesting if you got both SU(2)s from an SO(4), but why would the SU(2)s behave so differently? Maybe they both start complex, and one is reduced to real SU(2) for some reason and becomes the weak gauge field, and the other one stays complex and becomes Ashtekar gravity somehow.

how would Ashtekar gravity would arise from string theory via ambitwistor strings work out, are there any papers already on this?

there are a couple of papers, for example,

Gravitational origin of the weak interaction's chirality Stephon Alexander, Antonino Marciano, Lee Smolin arXiv:1212.5246

just to clarify,is it possible to express asymptotically Anti de Sitter (AAdS) spacetime in terms of Ashtekar gravity then apply AdS/CFT then apply Witten's paper, except replacing symptotically Anti de Sitter (AAdS) spacetime with the equivalent in Ashketar variables

Does Witten's paper provide a satisfactory quantization of gravity via AdS/CFT, if so, then does this lead to a successful quantum gravity with the Ashketar variables equivalent?

AdS/CFT originally was in 5 spacetime dimensions, and supersymmetric, is that what Witten is using in his paper?

Ashketar variables can have supersymmetry and generalized to 5 dimensions, but may not be physical.
 
  • #19
In the 2012 paper by Alexander et al, I see they start with a kind of topological field theory, which in its left-right symmetric phase gives a "bimetric" gravity (two metric fields), but which also has a broken symmetry phase where you get a metric coupled to an SU(2) gauge field. Or that's their claim.

I guess that's how you'd want things to work. And it might be tied up with the passage of gravity from a topological phase to a metric phase. E.g. the symmetric phase might be a purely topological "bigravity", but in the broken phase, one of the SU(2) fields somehow turns the topological manifold into a differentiable manifold by becoming the metric of Ashtekar gravity, and that provides the geometric arena for the other SU(2) field to become a proper Yang-Mills field.

Returning to the broader question of finding the right way to use Ashtekar variables in quantum gravity, I think one issue is UV completion. Loop quantum gravity tries to build the ultimate theory directly from the Ashtekar variables. Another perspective would be to say that there must be degrees of freedom beyond those in general relativity (because GR is non-renormalizable), the Ashtekar variables are just a way of rewriting GR (e.g. the 1998 Russian paper), and so quantum Ashtekar gravity is still just going to be an approximation to a deeper theory, such as string theory.

I mentioned ambitwistor strings. No one has related ambitwistors and Ashtekar variables to my knowledge. I mentioned the ambitwistors because Ashtekar variables seem to have some relationship to twistors, and the ambitwistors are a limit of string theory, from which you can derive the twistor formulae for field theories like Yang-Mills and gravity (see work by Yvonne Geyer). Also because the ambitwistors, unlike normal twistors, don't favor one chirality, so maybe they could even implement chiral graviweak unification.

Finally, about Witten's 2022 paper on canonical gravity in asymptotic AdS. He doesn't presuppose supersymmetry or any particular dimensionality. It's generally agreed that any gravitational theory in AdS should have a boundary dual... Basically he considers spacelike slices through AdS, and describes their quantum fluctuations using the BRST technique, in which you fix some properties of the field, and then define ghost fields which are allowed to fluctuate, and which act as proxies in the path integral for the property that has been fixed. In this case I think it's the timelike fluctuations of the AdS slice that have to get fixed, so you can have a quantum theory with a "c-number" (classical) time evolution.

The significance of Godazgar's 2017 paper, for me, was that he was applying some of the methods associated with twistors and Ashtekar variables (in his case, the "Sparling 3-form"), in the context of AdS/CFT. So it raised the possibility that Witten's 2022 AdS quantum gravity might be rewritten using Ashtekar variables. This was before I found the Russian paper, which did the substitution more directly. But the same remarks about UV completion still apply: Witten isn't saying that his canonical AdS gravity is UV complete, just that it's a viable perturbative approximation. You would still expect full quantum gravity in AdS, to include things like topology change that are inherently beyond his 2022 model.
 
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  • #20
One aspect of GR/QFT unification is surely about the relationship between classical and quantum models. Another aspect is renormalization. Yet another is whether we should approach constructing mathematical models in an operational and empiricist way or in a more realist theory-driven way.

In approximately reverse order, then, I've been approaching physics as a signal and data analysis formalism, starting about five years ago. In signal analysis we find a distinction between analysis of the real signal and analysis of the analytic signal that is interestingly comparable to the difference between classical and quantum models.

In measurement theory terms, there is an idea in the literature that we can have a Quantum Mechanics-free subsystem of QND measurements (see Tsang&Caves, open access, PRX 2012). A signal analysis approach further suggests an introduction of a new type of nonlinearity into the Wightman axioms, which also comes out a new analysis of renormalization.

To see how this can be filled out, insofar as I have so far done so, you could have a look at the talk I gave to the Lisbon Philosophy of Physics Seminar on May 17th or at the talk I gave to the NanoHubs Webinar on Nanotechnology on July 7th (at both of those YouTube links there is a Dropbox link to a PDF containing the slides, which in turn include links to published papers.) I'm giving a talk to the Mathematical Physics Seminar at the University of Iowa on September 19th, for which the title will be A Signal Reanalysis of Renormalization and the abstract will be

A signal and data analysis interpretation of quantum mechanics gives an effective way to understand the measurement problem and the renormalization 'problem'. In this talk I will first focus on renormalization, for which signal analysis suggests an introduction of a nonlinearity that is not in the literature as far as I know, although some other approaches can be understood to herald the idea. A reanalysis of real-space renormalization and of the renormalization group from this signal analysis perspective shows that this nonlinearity has always been present, but it is hidden differently in the two cases. I will present some new and I think interesting mathematical and physical ideas and questions that emerge.​
In the second part of the talk, in whatever time remains, I will discuss the measurement problem from a signal analysis perspective, which will be somewhat similar to material I presented to the UIowa MP seminar in April 2022, but refined by a number of other presentations of the same material elsewhere.​
If we want to figure out this stuff, I think it's likely we have to push out the boat a ways. In this new talk, I'll be focusing on renormalization more than I have in previous talks. The NanoHubs talk has a slight glitch at the beginning but otherwise I think it went better than the Lisbon talk, however some people may prefer the earlier talk's more philosophical slant.

Some people partially grok this, other people want something so different from what I'm reaching for that they might find not even a single idea in what I'm doing that they find useful. I'm coming out of a tradition in physics that is different enough from much of what is done in current work in quantum gravity that there may be no hope or it may change everything (every now and then I post something to PF because a question catches my fancy, then I sit back and see no engagement. In any case, best wishes to all in your own pursuit.)
 
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  • #21
Thread closed temporarily to sort out some member issues...
 
  • #22
After banning a sockpuppet of a previously banned member and cleaning up the posts, the thread is reopened. Thanks for your patience folks.
 
  • #23
mitchell porter said:
In the 2012 paper by Alexander et al, I see they start with a kind of topological field theory, which in its left-right symmetric phase gives a "bimetric" gravity (two metric fields), but which also has a broken symmetry phase where you get a metric coupled to an SU(2) gauge field. Or that's their claim.

I guess that's how you'd want things to work. And it might be tied up with the passage of gravity from a topological phase to a metric phase. E.g. the symmetric phase might be a purely topological "bigravity", but in the broken phase, one of the SU(2) fields somehow turns the topological manifold into a differentiable manifold by becoming the metric of Ashtekar gravity, and that provides the geometric arena for the other SU(2) field to become a proper Yang-Mills field.

Returning to the broader question of finding the right way to use Ashtekar variables in quantum gravity, I think one issue is UV completion. Loop quantum gravity tries to build the ultimate theory directly from the Ashtekar variables. Another perspective would be to say that there must be degrees of freedom beyond those in general relativity (because GR is non-renormalizable), the Ashtekar variables are just a way of rewriting GR (e.g. the 1998 Russian paper), and so quantum Ashtekar gravity is still just going to be an approximation to a deeper theory, such as string theory.

I mentioned ambitwistor strings. No one has related ambitwistors and Ashtekar variables to my knowledge. I mentioned the ambitwistors because Ashtekar variables seem to have some relationship to twistors, and the ambitwistors are a limit of string theory, from which you can derive the twistor formulae for field theories like Yang-Mills and gravity (see work by Yvonne Geyer). Also because the ambitwistors, unlike normal twistors, don't favor one chirality, so maybe they could even implement chiral graviweak unification.

Finally, about Witten's 2022 paper on canonical gravity in asymptotic AdS. He doesn't presuppose supersymmetry or any particular dimensionality. It's generally agreed that any gravitational theory in AdS should have a boundary dual... Basically he considers spacelike slices through AdS, and describes their quantum fluctuations using the BRST technique, in which you fix some properties of the field, and then define ghost fields which are allowed to fluctuate, and which act as proxies in the path integral for the property that has been fixed. In this case I think it's the timelike fluctuations of the AdS slice that have to get fixed, so you can have a quantum theory with a "c-number" (classical) time evolution.

The significance of Godazgar's 2017 paper, for me, was that he was applying some of the methods associated with twistors and Ashtekar variables (in his case, the "Sparling 3-form"), in the context of AdS/CFT. So it raised the possibility that Witten's 2022 AdS quantum gravity might be rewritten using Ashtekar variables. This was before I found the Russian paper, which did the substitution more directly. But the same remarks about UV completion still apply: Witten isn't saying that his canonical AdS gravity is UV complete, just that it's a viable perturbative approximation. You would still expect full quantum gravity in AdS, to include things like topology change that are inherently beyond his 2022 model.

1 what do you think about unifying weak force with Ashketar since both are SU(2) and how would electromagnetism enter this picture? Perhaps Kaluza Klein in 5 dimensions?2 the view LQG theorists is that while GR is nonrenormalizabl using standard perturbative QFT methods, it may be nonpertuberative renormalizeable.

3 you have a lot of faith in string theory

4

The significance of Godazgar's 2017 paper, for me, was that he was applying some of the methods associated with twistors and Ashtekar variables (in his case, the "Sparling 3-form"), in the context of AdS/CFT.

are there any papers that combines AdS/CFT with Ashtekar variables?

what is the CFT that is dual to Ashtekar variables in AdS?So it raised the possibility that Witten's 2022 AdS quantum gravity might be rewritten using Ashtekar variables.

What would be the implications of doing just that?

is there any possibility given gravity is gauge theory squared that 5 dimensional gravity in Ashtekar variables, joined with SU(2) weak force, is dual to 4 dimensional QCD squared via AdS/CFT with QCD written as a 4 dimensional CFT
 
  • #24
After reading arXiv:2308.03663 I am not satisfied with the conceptual stance to address this key question...

"A third problem concerns the question of why we want to define an algebra in the first place. What is this algebra supposed to mean? In ordinary quantum mechanics, an observer is external to the system and we are quite free to make what assumptions we want about the capability of the observer."

Witten writes
"a timelike worldline and we assume that what the observer can measure are the quantum fields along this worldline
...
As the simplest possible dynamical principle, we assume that the observer worldline is a geodesic. The model is meant to be an idealization of our own situation in the universe.
...
Of course, in a full theory of quantum gravity, we expect that an observer cannot be introduced from outside but must be described by the theory. What it means then to assume the presence of an observer is that we define an algebra that makes sense in a subspace of states in which an observer is present. We do not try to define an algebra that makes sense in all states."

He is again essential reducing the "observer" to sometime that is defined relative to a spacetime. I supposed this may be "hard enough", but it does not resolve the conceptual problems I think. For that reason the technical details withing that assumption are not very interesting to me, as it seems to me we need a more general way to represent this "internal observer". Ie. a geodesic wordline seems far from satisfactory.

/Fredrik
 
  • #25
In response to #23:

First, some AdS/CFT basics. You have a (conformal) quantum field theory on the AdS boundary. This gives rise to a variety of fields in the AdS bulk, according to what is called the AdS/CFT "dictionary". For each scalar quantity you can build out of the fields in the CFT, there's an emergent scalar field in the bulk. For each conserved current in the CFT, there's a bulk gauge field. The energy-momentum or stress-energy tensor of the CFT gives rise to the bulk graviton. Other combinations of CFT fields give rise to heavy bulk fields, excited string states, and so on.

One thing this makes clear is that the bulk fields aren't completely independent of each other. They are generated by different combinations drawn from the same set of ingredients, the fields in the boundary CFT.

The question is raised, what's the boundary dual of Ashtekar gravity, or of Ashtekar gravity coupled to an SU(2) gauge field. Well, Ashtekar gravity (at least classically) is supposed to be just general relativity with new variables, so it should still be dual to the CFT stress-energy tensor; and an SU(2) gauge field in the bulk, should be dual to an SU(2) current in the boundary CFT.

On the other hand, Ashtekar variables express general relativity as a kind of Yang-Mills theory, albeit one with no predefined metric. So you might anticipate that Ashtekar gravity also has to come from a conserved current on the boundary? Really, this is the kind of problem where you can't guess the answer in advance. You have to do the hard work of constructing the theory if you can, and then see what's left when you get to the end. The logic of AdS/CFT definitely implies that Ashtekar gravity in AdS should come from the stress-energy tensor of the boundary theory, but there may be some extra algebraic property implied by the existence of the Ashtekar formulation of gravity (in terms of connection variables rather than a metric).

The same goes for the common origin of SU(2)L and SU(2)R in a gauged SO(4), in chiral graviweak unification - AdS/CFT principles imply that it would come from an conserved SO(4) current on the boundary, but something is going to work differently, e.g. one is not starting with a predefined metric in the bulk, so perhaps one needs to consider a "topological AdS/CFT" which can generate a bulk topogical field theory, part of which then has a phase in which a metric emerges.
kodama said:
is there any possibility given gravity is gauge theory squared that 5 dimensional gravity in Ashtekar variables, joined with SU(2) weak force, is dual to 4 dimensional QCD squared via AdS/CFT with QCD written as a 4 dimensional CFT
Ashtekar variables are quite specific to 3+1 dimensions. Generalizing to higher dimensions, you lose some of their properties. So you would need to take care that your 5-dimensional variables, when reduced back to 4 dimensions by Kaluza-Klein compactification, still had all the properties that you want in your d=4 Ashtekar gravity.

The same applies to embedding SO(4) chiral graviweak unification in higher dimensions. Woit doesn't get the extra U(1) in this way, instead he wants to get an extra U(3) from a different source, that will provide both the extra U(1) of electroweak unification, and the SU(3) of QCD.

How any of this relates to double copy relations ("gravity is gauge theory squared"), is again something I can't guess without doing a lot more work. There has been some work on the double copy in AdS space, in which double copy relations between gauge field and gravity in the bulk, map onto relations among the dual operators on the boundary. The ingredients for a double copy relation still exist on the boundary: the dual of the bulk gauge field is a vector current, and a vector is a one-index tensor; meanwhile the dual of the gravitational field is the stress-energy tensor, which is a two-index tensor. So it makes sense that you can make a two-index tensor out of two copies of a one-index tensor. But double copy relations (from my reading) have a lot of finicky details, there isn't a simple template that you can apply to every situation.

But in this case, we are asked to think about double copies involving Ashtekar gravity, and that's the immediate challenge; coming up with a form of double copy relations that can apply to Ashtekar variables at all, never mind all the other details.

One last comment, QCD isn't a conformal theory, so it won't produce a simple AdS dual. When people talk about holographic QCD, they usually mean a construction (Sakai-Sugimoto-Witten) that isn't AdS at all. Though I think there is a "bottom-up holographic QCD" in which the dual is an AdS that is truncated or cut off.
 
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  • #26
mitchell porter said:
In response to #23:

First, some AdS/CFT basics. You have a (conformal) quantum field theory on the AdS boundary. This gives rise to a variety of fields in the AdS bulk, according to what is called the AdS/CFT "dictionary". For each scalar quantity you can build out of the fields in the CFT, there's an emergent scalar field in the bulk. For each conserved current in the CFT, there's a bulk gauge field. The energy-momentum or stress-energy tensor of the CFT gives rise to the bulk graviton. Other combinations of CFT fields give rise to heavy bulk fields, excited string states, and so on.

One thing this makes clear is that the bulk fields aren't completely independent of each other. They are generated by different combinations drawn from the same set of ingredients, the fields in the boundary CFT.

The question is raised, what's the boundary dual of Ashtekar gravity, or of Ashtekar gravity coupled to an SU(2) gauge field. Well, Ashtekar gravity (at least classically) is supposed to be just general relativity with new variables, so it should still be dual to the CFT stress-energy tensor; and an SU(2) gauge field in the bulk, should be dual to an SU(2) current in the boundary CFT.

On the other hand, Ashtekar variables express general relativity as a kind of Yang-Mills theory, albeit one with no predefined metric. So you might anticipate that Ashtekar gravity also has to come from a conserved current on the boundary? Really, this is the kind of problem where you can't guess the answer in advance. You have to do the hard work of constructing the theory if you can, and then see what's left when you get to the end. The logic of AdS/CFT definitely implies that Ashtekar gravity in AdS should come from the stress-energy tensor of the boundary theory, but there may be some extra algebraic property implied by the existence of the Ashtekar formulation of gravity (in terms of connection variables rather than a metric).

The same goes for the common origin of SU(2)L and SU(2)R in a gauged SO(4), in chiral graviweak unification - AdS/CFT principles imply that it would come from an conserved SO(4) current on the boundary, but something is going to work differently, e.g. one is not starting with a predefined metric in the bulk, so perhaps one needs to consider a "topological AdS/CFT" which can generate a bulk topogical field theory, part of which then has a phase in which a metric emerges.

Ashtekar variables are quite specific to 3+1 dimensions. Generalizing to higher dimensions, you lose some of their properties. So you would need to take care that your 5-dimensional variables, when reduced back to 4 dimensions by Kaluza-Klein compactification, still had all the properties that you want in your d=4 Ashtekar gravity.

The same applies to embedding SO(4) chiral graviweak unification in higher dimensions. Woit doesn't get the extra U(1) in this way, instead he wants to get an extra U(3) from a different source, that will provide both the extra U(1) of electroweak unification, and the SU(3) of QCD.

How any of this relates to double copy relations ("gravity is gauge theory squared"), is again something I can't guess without doing a lot more work. There has been some work on the double copy in AdS space, in which double copy relations between gauge field and gravity in the bulk, map onto relations among the dual operators on the boundary. The ingredients for a double copy relation still exist on the boundary: the dual of the bulk gauge field is a vector current, and a vector is a one-index tensor; meanwhile the dual of the gravitational field is the stress-energy tensor, which is a two-index tensor. So it makes sense that you can make a two-index tensor out of two copies of a one-index tensor. But double copy relations (from my reading) have a lot of finicky details, there isn't a simple template that you can apply to every situation.

But in this case, we are asked to think about double copies involving Ashtekar gravity, and that's the immediate challenge; coming up with a form of double copy relations that can apply to Ashtekar variables at all, never mind all the other details.

One last comment, QCD isn't a conformal theory, so it won't produce a simple AdS dual. When people talk about holographic QCD, they usually mean a construction (Sakai-Sugimoto-Witten) that isn't AdS at all. Though I think there is a "bottom-up holographic QCD" in which the dual is an AdS that is truncated or cut off.
thanks for this reply, it gives me a lot to think about.

yes, I am thinking along these lines,

joining the weak force (SU2) with Ashtekar gravity (SU2) to obtain SO(4) chiral graviweak unification

since the goal is the standard model coupled to gravity, we need U(1) so extend SO(4) chiral graviweak unification to 5 dimensions then do a Kaluza Klein compactification from 5 dimensions to 4, with the extra dimension a U(1) gauge charge.

then apply a kind of holographic relations with bottom-up holographic QCD in 4 dimensions, taking advantage of gauge-gravity double copy to get QCD and SU(3)

so SU(3) in 4D via holography and double copy, then SU(2) gravity and weak force and U(1) via Kaluza Klein in 5 dimensions

so U(1) exists as the fifth dimension curled up
SU(2) exists as weak force joined to gravity
SU(3) QCD exists as holographic duality in 4 dimensions and as double copy of gravity in 4 dimensions

Witten's paper gives ideas on how to quantize SU(2) ashketar gravity

supersymmetry hasn't been shown to exist and might not exist.

fermions are introduced by Bilson-Thompson braiding, in combination with clifford alegras and use of octonions to get 3 generations

the landscape is just 1 dimensions, matched to U(1) electromagnetism in the universe
 
  • #27
If I was pursuing chiral graviweak unification, I'd do a few things differently. The top-down inspiration might be what Woit's doing, but with octonionic supertwistors. But the more immediate goal would be to show that some version of the concept, is actually capable of giving you a functioning theory. Not the whole standard model plus gravity, but just gravity coupled to SU(2) Yang-Mills theory.

For example: we know how to start with Einstein metric-based gravity coupled to SU(2) Yang-Mills, and derive an effective field theory of gravitons coupled to massless SU(2) gauge bosons. Suppose we instead follow the procedure of Alexandrov and Vassilevich: start with a Hilbert-Palatini gravitational action, but now coupled to SU(2) Yang-Mills, and then change over to Ashtekar variables for the gravitational sector. What does that look like? Can you do perturbation theory? Can the whole thing be derived from e.g. "topological Yang-Mills theory" with SO(4) gauge group? If this minimal form can't be made to work, good luck making something even bigger...
 
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  • #28
mitchell porter said:
If I was pursuing chiral graviweak unification, I'd do a few things differently. The top-down inspiration might be what Woit's doing, but with octonionic supertwistors. But the more immediate goal would be to show that some version of the concept, is actually capable of giving you a functioning theory. Not the whole standard model plus gravity, but just gravity coupled to SU(2) Yang-Mills theory.

For example: we know how to start with Einstein metric-based gravity coupled to SU(2) Yang-Mills, and derive an effective field theory of gravitons coupled to massless SU(2) gauge bosons. Suppose we instead follow the procedure of Alexandrov and Vassilevich: start with a Hilbert-Palatini gravitational action, but now coupled to SU(2) Yang-Mills, and then change over to Ashtekar variables for the gravitational sector. What does that look like? Can you do perturbation theory? Can the whole thing be derived from e.g. "topological Yang-Mills theory" with SO(4) gauge group? If this minimal form can't be made to work, good luck making something even bigger...
what do you think could it be made to work?

this would only give SU(2) gravity in Ashketar variables and SU(2) weak force.

the reason I suggest 5 dimensions is to get Kaluza Klein theory and get electromagnetism, with just 1 only dimension compactified into a circle, instead of string theory 6 or 7 extra dimensions. but is there another way to get EM in just 4 dimensions. and also to get bottom-up holographic QCD in 4D
 
  • #29
mitchell porter said:
If I was pursuing chiral graviweak unification, I'd do a few things differently. The top-down inspiration might be what Woit's doing, but with octonionic supertwistors.
since it is octonic "super" twistors (Woit doesn't mention supersymmetry) couldn't you use previous papers on the use of octonions to get 3 generations with his theory?
 

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