Some of you may remember my Xtranormal video from a few years back “A Double Take on the String Wars.” Here it is if you missed it.

If you enjoyed that you will be pleased to know that there is a new sequel called “SYM and LQG: The Same Bloody Thing”

No offense intended to anyone who may accidentally resemble the characters in this video 🙂 This is just for fun.

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43 Responses to Super Yang-Mills vs Loop Quantum Gravity

Dear Phil, it’s interesting that although Rovelli’s accent sounds over the edge, it is so extremely similar to the way how the Italians speak in English.

The idea that it is the same bloody thing surely sounds politically correct but it is utterly unrealistic. There’s some overlap in the words and mathematical constructs but if you look what they do with them, you will see that they’re inequivalent and what Rovelli et al. doesn’t work while what Nima et al. does work…

Dear Lubos. I think you can see from some of the things in the video that I am not trying to be politically correct 😉 I agree that Loop Quantum Gravity does not work because it has not been able to recover locality, but I see it as a glass half full. I wont suggest that you see it as a glass half empty because I think you probably see it as less than that 🙂

I think the correspondence between the structures seen in LQG and SYM are more real and important than you suggest. The similarities are much stronger than I have indicated in this video if you look at them closely, but there are differences too. If people look at this correspondence they may be able to use it to make some progress but I worry that this will not happen for sociological reasons. Someone would need intimate knowledge of both theories but the people who work on them seem to be divided. I hope I am proved wrong.

From the more superficial level at which I see these things there are already some useful observations. I would say that one reason LQG is so incomplete is that the spin networks are based on only SU(2) which is half the Lorentz group. This happened I think because the canonical formalism splits time and space. In comparison to the SYM theory the spin networks have just the black nodes and not the white nodes because they effectively only use the lambdas and not the lambda-bars. The relationships between the loops and spin networks in LQG where the loops run through the nodes and links of the network is very similar indeed to lines running through the SYM on-shell diagrams and in both cases there are n-factorial inequivalent cases that need to be summed. The difference is that in SYM the lines turn left and right according to the colour of the node whereas in LQG they are braided and only one colour of node is used.

This also means that the LQG case has some features that SYM is missing because the lines are braided instead of just permuted. The SYM diagrams are representations of the Yangian for SL(4) from twistor space. The spin networks are representations of the quantum group SU_q(2), but the Yangian can be deformed and this is exactly what is required to turn it into a quantum group. It should be possible to bring the two cases together via representations of SL_q(4). Next the supersymmetric extension can be considered to see if it provides a consistent solution for scattering amplitudes where locality and causality are emergent.

Perhaps this might provide a scattering theory for something like N=8 SUGRA in 4D which has been described as being like two copies of N=4 SYM. This theory would subsume both SYM and LQG, but it is equally possible that this is a mirage and more new ideas are needed. There are already developments in N=8 SUGRA using twistors that I am not familiar with so perhaps these observations are already behind the state of the game. Others are also looking at twistors in LQG so I may be just pointing out obvious directions that are already being explored.

They are easy to make with Xtranormal. Unfortunately the website is closing down at the end of the month so I had to rush to make it which is why it is a bit rough.

Dear Phil, why don’t you write a paper if you think that there is a technical relationship, a way to benefit from the other set of ideas, and so on?

I did work on those things a decade ago, in the context of quasinormal modes and what became the most cited LQG papers of the year, and I was totally inspired by the possibility that there was something about the discreteness of areas or whatever LQG was suggesting. The response notwithstanding, the conclusion was still that there is *nothing* usable in the LQG toolkit.

If you were able to find something in LQG that actually works in QG or in twistor-based SYM calculations etc., that would be a very big discovery. I would bet anything that this won’t happen.

“I agree that Loop Quantum Gravity does not work because it has not been able to recover locality,” I have a working understanding of physics, including basic QFT, but I’m not up to date on this stuff. Could you summarize what you mean by this, or point me at a suitable reference? (There’s nothing about locality in the Wikipedia LQC article.)

Well if people would FINALLY learn a little category theory it would make much more sense. The symmetric structures (ie. permutations) come from a 4d category, which cannot exist without the 3d braided structures beneath it. The modern spin foams are of course nothing but a certain class of representation category, and there are plenty of string theorists who have worked with these – even using twistor techniques. Lubos is right – the twistor scattering picture is way ahead – even if they don’t get the importance of knots.

The basic problem with the analogy is that knotting occurs only in codimension 2. AdS/CFT strings do not therefore knot. Same applies to superstrings in general. The interpretation of strings in TGD framework is very different from that in QLG and superstring model.

String orbits in 3-D space/string world sheets in 4-D spacetime knot and also link/intersect so that string model in 4-D spacetime is the most interesting one and is indeed outcome of TGD. Also Yangian symmetries and their generalization and twistor picture emerge.

“Your text: 3076 characters, 442 words
Bullshit Index :1.26
Congratulations, you managed to blow up our index scale from 0 to 1. It is highly unlikely that you will impress anybody else, but you did manage to impress us!”

Supersymmetry can still be saved if we accept that shadow particles live entangled far away inside a copy anti material universe.
Then the big bang and the universe is still symmetric.
see
Wavefunction collapse and Human choice-making inside an entangled mirror symmetrical Multiverse. http://vixra.org/abs/1103.0015
3 Dimensional String Based Alternative Particles Model http://vixra.org/abs/1103.0002

Witten et al will never understand Langlands until they give up the idea that an action principle underlies the new physics. Arkani-Hamed gets this point, but he’s a bit of a mathematical imbecile.

Lol, yes. But Arkani-Hamed knows the physics and is working with some very good mathematicians. Also they do not give away all their insights and new ideas in public until they are finished with them.

The inside information is irrelevant, as interesting as it might be. The point is that they have decided that quantum gravity shall be Properly American – not for the benefit of the world.

I don’t think the current glass-bead games are going to benefit anyone. Benefits will germinate when people start studying nature again. We have seen where 40 years of glass-bead game playing have led us — nowhere, except to the foundation pit of the Tower of Babel.

Cool, it’s good to get the positive comment about it from Smolin in the questions. Skinner has done brilliant work for this talk. I noted the mention of resultants and discriminants. I think we may say hyperdeterminants there in the future, and then the realted generalised hypergeometric functions seem right for the poles at the corners of the polytopes

The quotient of Lie algebras e6/f4 is a vector space that can be
naturally identified with H3_0(O). That’s really cool!

But the quotient of Lie groups E6/F4 is what matters for the spin foam
models, and this is a bit “curvier” – it has a natural metric that’s
not flat.

They are closely related, however: e6/f4 can be viewed as a tangent
space of E6/F4.

A baby example of the same phenomenon is this:

sl(2,C)/su(2) = R^3, 3d flat space
SL(2,C)/SU(2) = H^3, 3d hyperbolic space.

This is what we get if we replace the Jordan algebra H3(O) by
the smaller Jordan algebra H2(C)…

>in my opinion such an H3_0(O) spin foam model
>should lead to,
>not just quantum gravity, but a Theory Of Everything.

Shhh! That’s supposed to be secret. 🙂

Yes, of course something like this is my goal, but I’m not eager
to count my chickens before they are hatched, nor take my ideas to
market while they’re still half-baked…

>The way I see it, there are three possibilities:
>
>1 – Superstring Theory is right.
>
>2 – Superstring Theory is wrong, but my D4-D5-E6 etc model is right.
>
>3 – Superstring Theory is wrong, and so is my D4-D5-E6 etc model.
>
>In 2 out of 3 cases,
>
>E6 / F4 = H3_0(O) Spin Foam Theory will be a big success.

At those odds, I guess I’d better get cracking. 🙂

back to me: Baez was responding to Tony Smith who answered:

It seems to me that what you want for a single bubble/component of foam
would be something that has two characteristics:

1 – the 24-dim 3-octonion structure of 26-dim H3(O)o

2 – associative structure so that you can
put a lot of bubbles together nicely

My candidate for that is the Clifford algebra Cl(8),

back to me: I also like Smith’s view that this could be related to a Garrett Lisi-like Loop Quantum Gravity model and that twistors are good for gravity not just Quantum Field Theory.

When your Platonism, or that of anybody you mention in the post, or that of anybody regularly speaking at conferences, can specify the exact nature of the dark matter, or convincingly retrodict the mass of the electron, please get back to me.

I wonder whether this is not just a new facet of a gauge/gravity duality going much deeper than AdS/CFT; similar things seem to pop up all over the place in recent years, whether it’s gravity (SUGRA) being ‘two copies’ of SYM, or gravity being described by renormalization group flows (for which there has been a recent argument in the case of Shape Dynamics), multiscale entanglement renormalization providing a ‘discrete’ realization of AdS/CFT, spacetime as being ‘glued together’ by entanglement (see Mark van Raamsdonk, and the recent ER=EPR ideas), Jacobson/Padmanabhan’s ideas about gravity as the thermodynamics of spacetime, and so on.

Perhaps the ‘induced gravity’ ideas by Sakharov from the sixties really mark the beginning of this trend, which also provides a realization of the ‘holographic’ motif underlying most of this: while it’s hard in general, it seems to be much easier to make sense of the idea that ‘Bekenstein-Hawking entropy is entanglement entropy’ in the case of induced gravity. Maybe all you need is an area law, and gravity comes for free. It certainly seems as if, after decades of lamenting the ‘inconsistency’ between gravity and the quantum, it seems hard these days to find a quantum theory that doesn’t have some form of gravitational ‘dual’ description…

I think what you are seeing is the slow re-emergence of Kaluza-Klein, much as though it was the convergence-point of all the dualities of the string landscape. Kaluza and Klein did have the Erlanger program behind them, which had reviewed many of the themes emerging recently through symmetry analysis.

And Roger “something must be dreadfully wrong” Penrose remains the quietly influential figure for having traced the problem from the d’Alembert wave equation and the awkward square root introduced by Dirac. AdS/CFT is. as it were, just a step back to the Huygens foundation, and seems necessary to wrap it all, as Steve Wolfram expects about now.

LOL!!! Very good!

Sometimes the truth is easier to process when it is presented in a comic form.

Great fun and spot on!

Dear Phil, it’s interesting that although Rovelli’s accent sounds over the edge, it is so extremely similar to the way how the Italians speak in English.

The idea that it is the same bloody thing surely sounds politically correct but it is utterly unrealistic. There’s some overlap in the words and mathematical constructs but if you look what they do with them, you will see that they’re inequivalent and what Rovelli et al. doesn’t work while what Nima et al. does work…

Cheers

LM

Dear Lubos. I think you can see from some of the things in the video that I am not trying to be politically correct 😉 I agree that Loop Quantum Gravity does not work because it has not been able to recover locality, but I see it as a glass half full. I wont suggest that you see it as a glass half empty because I think you probably see it as less than that 🙂

I think the correspondence between the structures seen in LQG and SYM are more real and important than you suggest. The similarities are much stronger than I have indicated in this video if you look at them closely, but there are differences too. If people look at this correspondence they may be able to use it to make some progress but I worry that this will not happen for sociological reasons. Someone would need intimate knowledge of both theories but the people who work on them seem to be divided. I hope I am proved wrong.

From the more superficial level at which I see these things there are already some useful observations. I would say that one reason LQG is so incomplete is that the spin networks are based on only SU(2) which is half the Lorentz group. This happened I think because the canonical formalism splits time and space. In comparison to the SYM theory the spin networks have just the black nodes and not the white nodes because they effectively only use the lambdas and not the lambda-bars. The relationships between the loops and spin networks in LQG where the loops run through the nodes and links of the network is very similar indeed to lines running through the SYM on-shell diagrams and in both cases there are n-factorial inequivalent cases that need to be summed. The difference is that in SYM the lines turn left and right according to the colour of the node whereas in LQG they are braided and only one colour of node is used.

This also means that the LQG case has some features that SYM is missing because the lines are braided instead of just permuted. The SYM diagrams are representations of the Yangian for SL(4) from twistor space. The spin networks are representations of the quantum group SU_q(2), but the Yangian can be deformed and this is exactly what is required to turn it into a quantum group. It should be possible to bring the two cases together via representations of SL_q(4). Next the supersymmetric extension can be considered to see if it provides a consistent solution for scattering amplitudes where locality and causality are emergent.

Perhaps this might provide a scattering theory for something like N=8 SUGRA in 4D which has been described as being like two copies of N=4 SYM. This theory would subsume both SYM and LQG, but it is equally possible that this is a mirage and more new ideas are needed. There are already developments in N=8 SUGRA using twistors that I am not familiar with so perhaps these observations are already behind the state of the game. Others are also looking at twistors in LQG so I may be just pointing out obvious directions that are already being explored.

Very interesting comment … 🙂

And wait a moment, do I understand this right and you made this very funny video …?

They are easy to make with Xtranormal. Unfortunately the website is closing down at the end of the month so I had to rush to make it which is why it is a bit rough.

Dear Phil, why don’t you write a paper if you think that there is a technical relationship, a way to benefit from the other set of ideas, and so on?

I did work on those things a decade ago, in the context of quasinormal modes and what became the most cited LQG papers of the year, and I was totally inspired by the possibility that there was something about the discreteness of areas or whatever LQG was suggesting. The response notwithstanding, the conclusion was still that there is *nothing* usable in the LQG toolkit.

If you were able to find something in LQG that actually works in QG or in twistor-based SYM calculations etc., that would be a very big discovery. I would bet anything that this won’t happen.

The geometric Langlands work by Witten et al might also be helpful as it concerns N=4 SYM and braiding.

Good point Kneemo, I’d forgotten that. I think there must be a Princeton masterplan that is gradually coming together

“I agree that Loop Quantum Gravity does not work because it has not been able to recover locality,” I have a working understanding of physics, including basic QFT, but I’m not up to date on this stuff. Could you summarize what you mean by this, or point me at a suitable reference? (There’s nothing about locality in the Wikipedia LQC article.)

Great post Phil! congratulations for you fun videos!

[…] At CERN, Amplitudes, Strings and Branes is on-going. Philip Gibbs has an amusing argument that this and Loops 13 are The Same Bloody Thing. […]

Well if people would FINALLY learn a little category theory it would make much more sense. The symmetric structures (ie. permutations) come from a 4d category, which cannot exist without the 3d braided structures beneath it. The modern spin foams are of course nothing but a certain class of representation category, and there are plenty of string theorists who have worked with these – even using twistor techniques. Lubos is right – the twistor scattering picture is way ahead – even if they don’t get the importance of knots.

I agree, category theory is the right tool, but the extra abstraction is hard for some physicists.

So because it’s hard for them, it’s OK for them to murder people?

The basic problem with the analogy is that knotting occurs only in codimension 2. AdS/CFT strings do not therefore knot. Same applies to superstrings in general. The interpretation of strings in TGD framework is very different from that in QLG and superstring model.

String orbits in 3-D space/string world sheets in 4-D spacetime knot and also link/intersect so that string model in 4-D spacetime is the most interesting one and is indeed outcome of TGD. Also Yangian symmetries and their generalization and twistor picture emerge.

For more details use “Knots and TGD” in google (my iPad does not allow to write the entire URL).

Regarding higher dimensions and supersymmetry, you might find this interesting.

Bee, Thanks for reminding me of this. The paper has had very few citations. I hope that will change eventually

Off topic, but your link to the blablameter (http://www.blablameter.com) made me test the obvious.

http://www.accenture.com/us-en/Pages/service-application-outsourcing-overview-summary.aspx

“Your text: 3076 characters, 442 words

Bullshit Index :1.26

Congratulations, you managed to blow up our index scale from 0 to 1. It is highly unlikely that you will impress anybody else, but you did manage to impress us!”

Supersymmetry can still be saved if we accept that shadow particles live entangled far away inside a copy anti material universe.

Then the big bang and the universe is still symmetric.

see

Wavefunction collapse and Human choice-making inside an entangled mirror symmetrical Multiverse.

http://vixra.org/abs/1103.0015

3 Dimensional String Based Alternative Particles Model

http://vixra.org/abs/1103.0002

Witten et al will never understand Langlands until they give up the idea that an action principle underlies the new physics. Arkani-Hamed gets this point, but he’s a bit of a mathematical imbecile.

Lol, yes. But Arkani-Hamed knows the physics and is working with some very good mathematicians. Also they do not give away all their insights and new ideas in public until they are finished with them.

Sort of like Nixon’s “secret plan” for ending the Vietnam war?

You mean like a conspiracy thing, yeah definitely is happening.

Yeah, they spend a lot of time reading my old blog.

Ahhhh, no. I mean like saying you have inside information that totally supports your position, but you won’t reveal it yet.

Oh, fer sur!

The inside information is irrelevant, as interesting as it might be. The point is that they have decided that quantum gravity shall be Properly American – not for the benefit of the world.

But quantum gravity is peanuts! What really makes an impact is the capability of using antimatter 😉

Marni, have you checked exotic smoothness and its relation with physics?

I don’t think the current glass-bead games are going to benefit anyone. Benefits will germinate when people start studying nature again. We have seen where 40 years of glass-bead game playing have led us — nowhere, except to the foundation pit of the Tower of Babel.

That’s more or less what I meant.

Phil, your video makes a cameo appearance here:

http://pirsa.org/displayFlash.php?id=13070064

Cool, it’s good to get the positive comment about it from Smolin in the questions. Skinner has done brilliant work for this talk. I noted the mention of resultants and discriminants. I think we may say hyperdeterminants there in the future, and then the realted generalised hypergeometric functions seem right for the poles at the corners of the polytopes

Nice. I never got any positive comments for anything – but I have found an impressive new Koide triplet.

From a 2001 John Baez sci.physics.research post:

The quotient of Lie algebras e6/f4 is a vector space that can be

naturally identified with H3_0(O). That’s really cool!

But the quotient of Lie groups E6/F4 is what matters for the spin foam

models, and this is a bit “curvier” – it has a natural metric that’s

not flat.

They are closely related, however: e6/f4 can be viewed as a tangent

space of E6/F4.

A baby example of the same phenomenon is this:

sl(2,C)/su(2) = R^3, 3d flat space

SL(2,C)/SU(2) = H^3, 3d hyperbolic space.

This is what we get if we replace the Jordan algebra H3(O) by

the smaller Jordan algebra H2(C)…

>in my opinion such an H3_0(O) spin foam model

>should lead to,

>not just quantum gravity, but a Theory Of Everything.

Shhh! That’s supposed to be secret. 🙂

Yes, of course something like this is my goal, but I’m not eager

to count my chickens before they are hatched, nor take my ideas to

market while they’re still half-baked…

>The way I see it, there are three possibilities:

>

>1 – Superstring Theory is right.

>

>2 – Superstring Theory is wrong, but my D4-D5-E6 etc model is right.

>

>3 – Superstring Theory is wrong, and so is my D4-D5-E6 etc model.

>

>In 2 out of 3 cases,

>

>E6 / F4 = H3_0(O) Spin Foam Theory will be a big success.

At those odds, I guess I’d better get cracking. 🙂

back to me: Baez was responding to Tony Smith who answered:

It seems to me that what you want for a single bubble/component of foam

would be something that has two characteristics:

1 – the 24-dim 3-octonion structure of 26-dim H3(O)o

2 – associative structure so that you can

put a lot of bubbles together nicely

My candidate for that is the Clifford algebra Cl(8),

back to me: I also like Smith’s view that this could be related to a Garrett Lisi-like Loop Quantum Gravity model and that twistors are good for gravity not just Quantum Field Theory.

When your Platonism, or that of anybody you mention in the post, or that of anybody regularly speaking at conferences, can specify the exact nature of the dark matter, or convincingly retrodict the mass of the electron, please get back to me.

I wonder whether this is not just a new facet of a gauge/gravity duality going much deeper than AdS/CFT; similar things seem to pop up all over the place in recent years, whether it’s gravity (SUGRA) being ‘two copies’ of SYM, or gravity being described by renormalization group flows (for which there has been a recent argument in the case of Shape Dynamics), multiscale entanglement renormalization providing a ‘discrete’ realization of AdS/CFT, spacetime as being ‘glued together’ by entanglement (see Mark van Raamsdonk, and the recent ER=EPR ideas), Jacobson/Padmanabhan’s ideas about gravity as the thermodynamics of spacetime, and so on.

Perhaps the ‘induced gravity’ ideas by Sakharov from the sixties really mark the beginning of this trend, which also provides a realization of the ‘holographic’ motif underlying most of this: while it’s hard in general, it seems to be much easier to make sense of the idea that ‘Bekenstein-Hawking entropy is entanglement entropy’ in the case of induced gravity. Maybe all you need is an area law, and gravity comes for free. It certainly seems as if, after decades of lamenting the ‘inconsistency’ between gravity and the quantum, it seems hard these days to find a quantum theory that doesn’t have some form of gravitational ‘dual’ description…

I think what you are seeing is the slow re-emergence of Kaluza-Klein, much as though it was the convergence-point of all the dualities of the string landscape. Kaluza and Klein did have the Erlanger program behind them, which had reviewed many of the themes emerging recently through symmetry analysis.

And Roger “something must be dreadfully wrong” Penrose remains the quietly influential figure for having traced the problem from the d’Alembert wave equation and the awkward square root introduced by Dirac. AdS/CFT is. as it were, just a step back to the Huygens foundation, and seems necessary to wrap it all, as Steve Wolfram expects about now.

Does anybody wonder why galaxies tend to populate 3 basic categories: elliptical, disk, and irregular?

You can keep making videos like these after XN shuts down. Come here for more info.

http://groups.yahoo.com/group/emergent-animation

西边的太阳就要落山了

The article is written in Italian, but I’ll try to summarize: Carlo Rovelli is heading to Mars. Literally.

Italian physicist Carlo Rovelli is heading to #Mars. Really. http://www.corriere.it/tecnologia/cyber-cultura/13_settembre_17/italiani-marte-viaggio_2f253a3e-1f6b-11e3-9636-b0708204026a.shtml