Alexander paper - CP and lambda

[Kea]

How about we start a thread on the Stephon Alexander paper, too.

A Quantum Gravitational Relaxation of The Cosmological Constant
Stephon Alexander
6 pages
http://www.arxiv.org/abs/hep-th/0503146

"Similar to QCD, general relativity has a $\Theta$ sector due to large diffeomorphisms. We make explicit, for the first time, that the gravitational CP violating $\Theta$ parameter is non-perturbatively related to the cosmological constant. A gravitational pseudoscalar coupling to massive fermions gives rise to general relativity from a topological $B\wedge F$ theory through a chiral symmetry breaking mechanism. We show that a gravitational Peccei-Quinn like mechanism can dynamically relax the cosmological constant."

 

[nightcleaner]

I would like to read this paper, if only I could. Well, I can read some of the English part. Perhaps I can make a start if Kea, you or someone could tell me what the $\Theta$ means. It looks to me like a code similar to our laTex, so I imagine the reference is to a $$\Theta$$ (-sector, -parameter). I don't have any idea what the wedge thingy would be.

I read some notes about CP violation, but I will have to look at them again. Chiral rhymes with spirol, and do I remember some anatomy about a chiral fracture? It twists around the bone. I will have to find our what Peccei Quinn like mechanism is.

So, off to the races. Any hints will be gratefully recieved. Thanks,

nc

 

[selfAdjoint]

$B \wedge F$ is $$B \wedge F$$, a part of the lagrangian for BF theory. General relativity is a BF theory plus some other stuff. Chiral is from the Greek word for hand, which is where the fracture name comes from, but in this context it refers to the handedness of particles, relating to their spin, right-handed or left-handed.

 

[nightcleaner]

Great thanks, selfAdjoint.

I found this:

http://www.phys.ufl.edu/~korytov/phy2049/new_notes/chapter_24.pdf

good stuff for us duffers trying to learn to read Maxwell and Gauss equations. Nice conceptual pictures. Comic book physics, I guess.

So I guess B is magnetic field, and F would be force. Now Lagrangian, I know I've read about that before. Let's see...

I read a couple articles, Wiki and Eric Weistein and one other. Still have only a foggy notion, something about subtracting the potential from the kinetic energy of a system.

No sign of the wedge yet. I would guess it is from set theory, a special case of the cup or union?

I found this:

https://www.physicsforums.com/archi...basic_to_LQG_so_we_should_learn_about_it.html

a cached discussion about the B wedge F theory, with Marcus and Chronos.

 

[marcus]

How about we start a thread on the Stephon Alexander paper, too.

I suspect Kea of (what is the verb, plug, boost?) spotlighting her friends work didnt she co-author something with him?
Speaking of those Stephon has papers with, IIRC he has written several with Lee Smolin on LQG related themes. Something about cosmology and the Kodama state.

Stephon has a blog. I seem to remember that he is an amateur jazz musician among other accomplishments. Well let's get back on topic, what is this paper about, in layman's terms, if anyone would like to take the trouble to tell us?

 

[selfAdjoint]

Great thanks, selfAdjoint.

I found this:

http://www.phys.ufl.edu/~korytov/phy2049/new_notes/chapter_24.pdf

good stuff for us duffers trying to learn to read Maxwell and Gauss equations. Nice conceptual pictures. Comic book physics, I guess.

So I guess B is magnetic field, and F would be force. Now Lagrangian, I know I've read about that before. Let's see...

I read a couple articles, Wiki and Eric Weistein and one other. Still have only a foggy notion, something about subtracting the potential from the kinetic energy of a system.

No sign of the wedge yet. I would guess it is from set theory, a special case of the cup or union?

I found this:

https://www.physicsforums.com/archi...basic_to_LQG_so_we_should_learn_about_it.html

a cached discussion about the B wedge F theory, with Marcus and Chronos.

B is designated by that letter beause it behaves like a magnetic field, but it isn't actually one. F can be thought of as a force, but its actual definition is as the curvature of a connection. Sadly, it gets deeper and deeper. They are both forms and the $$B \wedge F$$ is their outer product, making a new form of higher degree. Pure BF theory is like a simplified version of electromagnetism, and used to be just a toy theory until it was discovered that general relativity can be described as a "kicked" BF theory.

 

[selfAdjoint]

Here's the money graf from the paper

Specifically, we will demonstrate that a Peccei-Quinnlike
mechanism associated with a non-vanishing vev of
fermion bilinears coupled to gravity will yield an effective
potential for a parameter which alters the ratio of
Barbero-Immirizi parameter and the cosmological constant.
We then use the value of the Barbero-Immirizi parameter
determined from Black Hole quasinormal modes
to determine the conditions which relaxes the cosmological
constant. This mechanism is deeply tied to the presence
of gravitational instantons in the state space of Loop
Quantum Gravity which arise naturally as exact solutions
of the (anti)self dual formulation of general relativity

Anybody want to discuss it?

 

[marcus]

Here's the money graf from the paper



Anybody want to discuss it?

selfAdjoint have you spent money again to get a key paper. if so it is darn public spirited. thankyou
(I guessed, wrongly, that a "money graf" is a portmanteau word for a monograph that you have to pay for.)

[EDIT]now I get it, the moneygraph is the PARAGRAPH which contains the meat of the article and which is "on the money"[/EDIT]

 

[marcus]

this Stephon paper has several references to the
recent Freidel Starodubtsev.
Kea knows both Freidel and Starodubtsev and took the trouble to say how nice they are. My impression is she knows a lot of these younger LQG people.

We had some discussion a year or so ago at PF of the
Smolin, Alexander, Malecki
Quantum Gravity and Inflation
http://arxiv.org/hep-th/0309045
this was another one of those stubborn papers that think the kodama state points to a good ground state. despite witten's condemnation of kodama.

I am interested that the kodama state keeps surfacing despite witten's criticism. also I admire Stephon Alexander's nerve
here he is writing this paper which is devoting the entire third paragraph of the "Conclusions" section at the end to the kodama state.
and a couple of weeks ago he posted this other paper about Kodama state with a couple of Canadians,

http://arxiv.org/abs/gr-qc/0503062
Fermionic sectors for the Kodama state
Stephon Alexander, Kristin Schleich, Donald M. Witt
4 pages
SLAC-PUB-10841

"Diffeomorphisms not connected to the identity can act nontrivially on the quantum state space for gravity. However, in stark contrast to the case of nonabelian Yang-Mills field theories, for which the quantum state space is always in 1 dimensional representation of the large gauge transformations, the quantum state space for gravity can have higher dimensional representations. In particular, the Kodama state will have 2 dimensional representations, that is sectors with spin 1/2, for many topologies that admit positive scalar curvature. The existence of these spin 1/2 states are used to point out a possible answer to certain criticisms raised recently in the literature."

 

[selfAdjoint]

selfAdjoint have you spent money again to get a key paper. if so it is darn public spirited. thankyou
(I guessed, probably wrongly, that a "money graf" is a portmanteau word for a monograph that you have to pay for.)

if so, I do not see an attachment

Sorry about that. I thought people would recognize that "money graf" is reporter slang for key paragraph, locus of the core of the information.

 

[marcus]

Here's the money graf from the paper

Specifically, we will demonstrate that a Peccei-Quinnlike
mechanism associated with a non-vanishing vev of
fermion bilinears coupled to gravity will yield an effective
potential for a parameter which alters the ratio of
Barbero-Immirizi parameter and the cosmological constant.
We then use the value of the Barbero-Immirizi parameter
determined from Black Hole quasinormal modes
to determine the conditions which relaxes the cosmological
constant. This mechanism is deeply tied to the presence
of gravitational instantons in the state space of Loop
Quantum Gravity which arise naturally as exact solutions
of the (anti)self dual formulation of general relativity

Anybody want to discuss it?

sure, for starters let us just parse it a little

VEV is vacuum expectation value, etc etc get the simple things clear
I am puzzled by the part where he says "This mechanism is deeply tied to the presence of gravitational instantons in the state space of Loop Quantum Gravity..." It seems to have something to do with the 1977 paper of Peccei and Quinn CP conservation in the presence of instantons that he cites as reference [4]. I do not know from instantons.

 

[marcus]

Stephon's paper is mostly out of reach for me.

I noticed a possible typo though, in equation (26) it seemed reasonable to suppose that he means to write 1152 instead of 1154.
Maybe I will email him and ask for confirmation. but it is trivial.

 

[Chronos]

An interesting approach. The paper is pretty math intense, making it a little hard to absorb for lazy people like me. Resolving the cosmological constant problem - which arises due to background dependence - using BF theory struck me as ironic. But Peccei-Quinn theory nicely takes care of the strong CP problem, so it is a very natural and attractive approach. I will be a lot more comfortable with it when axions are detected. I'm a little troubled by the severe mass constraints, but hopefully SQUID will come through and save the day. Axion detection would be huge. Talk about go pick up your Nobel.

 

[Chronos]

Stephon's paper is mostly out of reach for me.

I noticed a possible typo though, in equation (26) it seemed reasonable to suppose that he means to write 1152 instead of 1154.
Maybe I will email him and ask for confirmation. but it is trivial.

I agree, 1154 can't be right. You wouldn't think it was trivial if it were your paper, would you?

 

[marcus]

It is trivial, but I wrote him email a while ago, asking about 1154 versus 1152. Maybe he wants help catching typos.

 

[marcus]

Stephon's paper is mostly out of reach for me.
...

Kodama state keeps coming up (altho Witten canned it in 2003)

it is in the conclusions of this Stephon paper and also it is in a paper Stephon wrote the month before with Kristin Schleich and Don Witt

and now today we have this:
http://arxiv.org/abs/hep-th/0504120
The Kodama state for topological quantum field theory beyond instantons
R. Cartas-Fuentevilla, J. F. Tlapanco-Limon
8 pages. submitted to physics letters B

"Constructing a symplectic structure that preserves the ordinary symmetries and the topological invariance for topological Yang-Mills theory, it is shown that the Kodama (Chern-Simons) state traditionally associated with a topological phase of unbroken diffeomorphism invariance for instantons, exists actually for the complete topological sector of the theory. The case of gravity is briefly discussed."

Notice that it is not primarily about gravity. Maybe it is not important, but it is straws in the wind. Kodama state still interests people (like Stephon Alexander, like these two people I never heard of before)

Here is an earlier (Kristin Schleich) Kodama thread, if anyone is curious about that paper as well:
https://www.physicsforums.com/showthread.php?t=67424

 

[Haelfix]

Yea this is a very interesting paper, and a very nice attempt. I've always been a firm believer of the axion particle (even if it has resisted detection).

Jacques Distler on his blog wrote up some counter arguments to it. Basically he liked the idea, but was a little skeptical of applying that particular GR approach to a quantum theory, as it omits various terms relevant to the SO(5) symmetry. When you do that, the theta term loses its control over the cosmological constant (they are no longer linked).

 

[ohwilleke]

Sorry about that. I thought people would recognize that "money graf" is reporter slang for key paragraph, locus of the core of the information.

Ah, but this is physics forums and most of the dezinens are geeks.

 

[marcus]

Here is the link, again, to the Stephon Alexander paper, just to have it handy.

http://arxiv.org/hep-th/0503146

Here are the first two paragraphs of Stephon's paper
They are interesting because they give an overview of how he sees his paper, where it fits in, and what the main thrust of it is.

---Alexander paper Intro, first two paragraphs---

It has always been a dream to solve the cosmological constant problem by relaxing it to the minimum of a potential [1]. This hope has been especially unsuccessful in conventional canonical quantum gravity. In QCD, the strong CP problem was solved by relaxing the Theta parameter at the minimum of the potential associated with an axion field via the Peccei-Quinn mechanism. It turns out that when quantum gravity is formulated in the Ashtekar-Sen variables (LQG), the theory has a semblance to Yang-Mills theory and the cosmological constant problem becomes analogous to the strong CP problem. It is the purpose of this paper to make this analogy explicit and use a Peccei-Quinn like mechanism to pave a possible route to solving the cosmological constant problem.

Loop Quantum Gravity (LQG) has a one parameter family of ambiguities which is labeled by $$\gamma$$, the Barbero Immirizi parameter. This parameter plays a similar role to the QCD Theta parameter which labels the unitarily inequivalent sectors of the quantum theory. These sectors can be accessed by tunneling events due to instanton field configurations. Theta is also a measure of CP violation, which is constrained by the neutron electric dipole moment to be Theta < 10^-9.

In LQG the Barbero-Immirizi parameter is also a measure of CP violation, since it couples to the first Pontrjagin class. Specifically, in the quantum theory $$\gamma$$ corresponds to unitarily inequivalent representations of the algebra of geometric operators. For example, the simplest eigenvalues of the area operator in the $$\gamma$$ quantum sector is given by

[familiar LQG formula for area eigenvalues]

What fixes the value of the Barbero-Immirizi parameter? In this letter we will show that this question is connected to another parameter in general relativity, the cosmological constant.

Therefore the question of fixing the Barbero-Immirizi parameter is related to a quantum gravitational determination of the cosmological constant. Through this relationship we will propose a possible dynamical, background independent mechanism to relax the cosmological constant. Specifically, we will demonstrate that a Peccei-Quinn like mechanism associated with a non-vanishing vev of fermion bilinears coupled to gravity will yield an effective potential for a parameter which alters the ratio of Barbero-Immirizi parameter and the cosmological constant.

We then use the value of the Barbero-Immirizi parameter determined from Black Hole quasinormal modes to determine the conditions which relaxes the cosmological constant.

---end quote---

 

[ohwilleke]

Let me take a stab at explaining what is going on in this paper in terms more familiar to a generalist physicist audience.

The single most important thing to understand about this paper is that it is part of a larger program of theoretical research to unify QCD and a loop quantum gravity verson of quantum gravity in much the same way that the electro-magnetic force and the weak force have been unified already. In other words, this paper is arguing that gravity is basically the flip side of the nuclear strong force (or at least, that it is very similar in theoretical structure to the strong force). This paper is applying QCD concepts to quantum gravity by analogy and seeing what results flow from it. The QCD analogy is an important one, because QCD operates very differently at different scales, which implies that gravity should do the same in an inverse sort of way (i.e. acting very differently at very large scales such as cosmological ones, instead of the very small scales of QCD).

The next big thing to observe is the Stot=Sg + Sd + So decomposition of gravity with Sg further divided into Sp and Scp. This is a tensor-vector-scalar version of gravity in which Sg provides the complete GR with cosmological constant tensor formulation, Sd describes a vector field, and So describes a pseudo-scalar field. (In this way it is similar to Bekenstein's TeVeS version of MOND that eliminates the need for dark matter, although the formulation is a little closer to some other and similar alternative GR gravity ideas).

They identify Sp with the Palatini action in general relativity with a non-zero cosmological constant. They identify the other part of Sg (i.e. the tensor GR based part of loop quantum gravity) which they call Scp with the charge-parity violating theta term in QCD and change their notation from that of equation (13) to that of equation (14) to make the parallel more striking by defining a theta term in the LQG equations in a manner similar to that in the QCD equations.

They explain that theta corrosponds in loop quantum gravity to "a one parameter family of vacuum states" (i.e. it corrosponds to form of zero point energy in quantum gravity). And, it shows from these equations that theta, a vacuum state constant, is inversely related to the cosmological constant.

Then, the analysis moves on to the vector field of LQG. It argues that it is the coupling of mass with the vector field results in a non-zero theta which is related to the cosmological constant and the Immizri parameter from Sg (which is like the way theta produces CP violations from the coupling of quark masses in Yang-Mills theory in QCD). It goes on to state that following the conclusions of Peccei, Quinn, Weinberg and Wilczek that a pseudo-scalar field associated with a light spin zero particle called the axion can keep CP violations from vector field getting out of control in QCD. They then reason that a similar mechanism will work naturally in quantum gravity to keep the cosmological constant from getting crazy large. (The big mystery of dark energy theory is cosmology is why the QED predictions of zero point energy differ by so many orders of magnitude from the dark energy amounts predicted by empirical measurements of the apparent cosmological constant and this paper used LQG ideas to try to suggest a mechanism for reconcilling the two).

The next section develops the pseudoscalar field in LQG by analogy with the QCD axion field (and notes that the pseudoscalar field is related to Weyl spinors from GR). Incidentally, this section also starts to draw upon the hypothesis that in LQG the coupling of gravity to fermions is parity dependent. This section explains how the pseudoscalar field creates a ground state in LQG which "eats up" the true cosmological constant leaving a much smaller effective cosmological constant.

From this analysis, the paper then draws the conclusion that the ground state of the cosmological constant (i.e. the minimum density of dark energy in the universe from ZPE) does not gravitate and that the cosmological constant flows only from the gravitation of variations in dark energy concentrations from place to place within space.

The paper then concludes with two speculations. First, it notes that a Kodoma State (which can corrospond to quantum gravity with a cosmological constant, and can also corospond to de Sitter space) with a scalar field gives rise to cosmological inflation, and goes on to speculate that the gravitation related light spin zero particles it calls gravitational axions could give rise to such a scalar field. And, then, it make a second speculation related to Alexander, Mbonye and Moffat's paper called "The Gravitational Instability of the Vacuum: Insights into the Cosmological Constant Problem", which relates the way instability in UV scale graviton exchange (i.e. strong gravitational fields) can be related to quantum behavior in superconductors because peturbative physics approaches no longer work in both cases and the ground state analysis relied upon in this paper no longer applies in those situations because a "true ground state is reached".

I started out calling this summary a "layman's explanation" but it is clearly not that. However, I do think it does spell out the broad brushes of what is going on in the paper.

 

[marcus]

this is interesting and helpful, willeke, thanks for posting it!

 

[ohwilleke]

A nice discussion of axions is found here:

http://web.mit.edu/~redingtn/www/netadv/specr/345/node3.html

 

[wolram]

http://www.phys.washington.edu/colloquia/spring05.pdf

Leslie Rosenberg LLN Laboratory
Searching for Dark Matter Axions April 4

This little snippet suggests that the Axion has no where to hide if it
exists,

 

[selfAdjoint]

http://www.phys.washington.edu/colloquia/spring05.pdf

Leslie Rosenberg LLN Laboratory
Searching for Dark Matter Axions April 4

This little snippet suggests that the Axion has no where to hide if it
exists,

And on the other hand, they will be able to say definitely whether it doesn't exist.

 

[marcus]

Reminding everybody of the long discussion of Stephon's paper and the Freidel Starodubtsev paper, which took place here
http://golem.ph.utexas.edu/~distler/blog/archives/000541.html
at Jaques Distler blog

Here for reference is Stephon's paper again
http://arxiv.org/hep-th/0503146

Here is the link for the Freidel Starodubtsev one (we had a thread about it at PF in which John Baez took part)

https://www.physicsforums.com/showthread.php?t=61041

http://arxiv.org/abs/hep-th/0501191
Quantum gravity in terms of topological observables
Laurent Freidel, Artem Starodubtsev

"We recast the action principle of four dimensional General Relativity so that it becomes amenable for perturbation theory which doesn't break general covariance. The coupling constant becomes dimensionless $${(G_{Newton} \Lambda)}$$ and extremely small $$10^{-120}$$ . We give an expression for the generating functional of perturbation theory. We show that the partition function of quantum General Relativity can be expressed as an expectation value of a certain topologically invariant observable. This sets up a framework in which quantum gravity can be studied perturbatively using the techniques of topological quantum field theory."

since we are gathering thematic material together I will repeat
the first two paragraphs of Stephon's paper.
They give an overview, which supplements that given by Ohwilleke, of how Stephon sees his paper, where it fits in, and what the main thrust of it is.

---Alexander paper Intro, first two paragraphs---

It has always been a dream to solve the cosmological constant problem by relaxing it to the minimum of a potential [1]. This hope has been especially unsuccessful in conventional canonical quantum gravity. In QCD, the strong CP problem was solved by relaxing the Theta parameter at the minimum of the potential associated with an axion field via the Peccei-Quinn mechanism. It turns out that when quantum gravity is formulated in the Ashtekar-Sen variables (LQG), the theory has a semblance to Yang-Mills theory and the cosmological constant problem becomes analogous to the strong CP problem. It is the purpose of this paper to make this analogy explicit and use a Peccei-Quinn like mechanism to pave a possible route to solving the cosmological constant problem.

Loop Quantum Gravity (LQG) has a one parameter family of ambiguities which is labeled by $$\gamma$$, the Barbero Immirizi parameter. This parameter plays a similar role to the QCD Theta parameter which labels the unitarily inequivalent sectors of the quantum theory. These sectors can be accessed by tunneling events due to instanton field configurations. Theta is also a measure of CP violation, which is constrained by the neutron electric dipole moment to be Theta < 10^-9.

In LQG the Barbero-Immirizi parameter is also a measure of CP violation, since it couples to the first Pontrjagin class. Specifically, in the quantum theory $$\gamma$$ corresponds to unitarily inequivalent representations of the algebra of geometric operators. For example, the simplest eigenvalues of the area operator in the $$\gamma$$ quantum sector is given by

[familiar LQG formula for area eigenvalues]

What fixes the value of the Barbero-Immirizi parameter? In this letter we will show that this question is connected to another parameter in general relativity, the cosmological constant.

Therefore the question of fixing the Barbero-Immirizi parameter is related to a quantum gravitational determination of the cosmological constant. Through this relationship we will propose a possible dynamical, background independent mechanism to relax the cosmological constant. Specifically, we will demonstrate that a Peccei-Quinn like mechanism associated with a non-vanishing vev of fermion bilinears coupled to gravity will yield an effective potential for a parameter which alters the ratio of Barbero-Immirizi parameter and the cosmological constant.

We then use the value of the Barbero-Immirizi parameter determined from Black Hole quasinormal modes to determine the conditions which relaxes the cosmological constant.

---end quote---

In light of all this it is fascinating to see how Jacques Distler who has devoted much of his career to string theorizing and has what is probably the best string blog, responds to the papers of Stephon and of Laurent Freidel. Lee Smolin also takes part in the thread responding to questions and requests for information from Distler.

this kind of intense string interest in LQG at the detail level and accordingly intense exchanges were rare heretofore---or else were rather noisy occasions

 

[ohwilleke]

since we are gathering thematic material together I will repeat the first two paragraphs of Stephon's paper.

Good post. Bad paragraph counting.

 

[marcus]

Good post. Bad paragraph counting.

thanks. Oh I see: there was an indentation after the equation, so it is the first THREE paragraphs. sorry for the miscount.

 

[wolram]

By MARCUS


Loop Quantum Gravity (LQG) has a one parameter family of ambiguities which is labeled by LaTeX graphic is being generated. Reload this page in a moment., the Barbero Immirizi parameter. This parameter plays a similar role to the QCD Theta parameter which labels the unitarily inequivalent sectors of the quantum theory. These sectors can be accessed by tunneling events due to instanton field configurations. Theta is also a measure of CP violation, which is constrained by the neutron

Can someone explain "tunneling", please.

 

[marcus]

wolram you are quoting Stephon Alexander, apparently you were not getting the greek letter gamma so I will fill in where you had trouble:

Loop Quantum Gravity (LQG) has a one parameter family of ambiguities which is labeled by gamma, the Barbero Immirizi parameter. This parameter plays a similar role to the QCD Theta parameter which labels the unitarily inequivalent sectors of the quantum theory. These sectors can be accessed by tunneling events due to instanton field configurations. Theta is also a measure of CP violation, which is constrained by the neutron...

your question about the QCD Theta parameter is not a question about LQG but about Quantum Chromodynamics, so I will leave it for someone more expert in QCD.

Would anyone like to clarify this: "...QCD Theta parameter which labels the unitarily inequivalent sectors of the quantum theory. These sectors can be accessed by tunneling events due to instanton..."?

what interested me in these introductory paragraphs of the paper is that it makes explicit, in his own words, something that Ohwilleke said earlier. there is an initiative in progress now to UNIFY LQG WITH QCD. You can see from the number of references to LQG here that the paper really is about LQG but on the other hand it is also about stuff over in the QCD court as well, clearly. I didn't realize to what an extent this was going on. So this paper is, for me, venturing into unfamiliar territory.

Likewise, to some extent, the Freidel Starodubtsev, and Freidel Livine papers that came out recently. one of which Stephon Alexander cites.

 

[wolram]

By MARCUS


what interested me in these introductory paragraphs of the paper is that it makes explicit, in his own words, something that Ohwilleke said earlier. there is an initiative in progress now to UNIFY LQG WITH QCD. You can see from the number of references to LQG here that the paper really is about LQG but on the other hand it is also about stuff over in the QCD court as well, clearly. I didn't realize to what an extent this was going on. So this paper is, for me, venturing into unfamiliar territory.

I have read a little on high energy phys, some papers do mention LQG but
i could only understand parts of them, i hope this is a marriage made in
heaven, LQGQCD or QCDLQG?

 

[marcus]

I have read a little on high energy phys, some papers do mention LQG but
i could only understand parts of them, i hope this is a marriage made in
heaven, LQGQCD or QCDLQG?

wolram, it seems to me quite a recent initiative with no indication whether or not it will eventually work out (but that is the most exciting part of a relationship anyway, probably)

we both could learn by going over Ohwilleke post #20 again---he spells it out with more detail and it is really his observation

https://www.physicsforums.com/showpost.php?p=530777&postcount=20


One point to clarify, I guess. LQG since its very beginning has looked like a non-abelian gauge theory, or like a generalized Yang-Mills theory with SU(2) standing in for U(1). My understanding is that this was thanks to the Ashtekar-Sen formulation in 1986 which focused on the connection (rather than the metric). So when Rovelli and Smolin worked out LQG in the early 1990s they were consciously using the gauge theory that was fashionable in particle physics (for example QCD) as a model.

I think what Ohwilleke was talking about in the post I mentioned is not the OLD connection by analogy, but something new that is currently in progress.

 

[ohwilleke]

This paper on the connection between QCD and gravity is particularly notable in my mind:

Date: Wed, 17 Sep 2003 05:42:53 GMT (7kb)

Non-Abelian Effects in Gravitation
Authors: A. Deur
Comments: 3 pages, no figure

The non-abelian symmetry of a lagrangian invalidates the principle of superposition for the field described by this lagrangian. A consequence in QCD is that non-linear effects occur, resulting in the quark-quark linear potential that explains the quark confinement, the quarkonia spectra or the Regge trajectories. Following a parallel between QCD and gravitation, we suggest that these non-linear effects should create an additional logarithmic potential in the classical Newtonian description of gravity. The modified potential may account for the rotation curve of galaxies and other problems, without requiring dark matter.

http://arxiv.org/abs/astro-ph/?0309474

Any time you see a mention of Yang-Mills in a LQG paper, you are seeing a reference to a core theory of QCD. This paper (http://www.claymath.org/millennium/Yang-Mills_Theory/Official_Problem_Description.pdf 15 page pdf) lays out the connection nicely. This Wikipedia article: http://wikipedia.findthelinks.com/mi/Millennium_Prize_Problems.html explains that progress related to Yang-Mills has been identified as one of the top ten issues in mathematics right now and that solving related problems will earn you $1,000,000. The connection between Yang-Mills and QCD is also discussed in this Wikipedia article: http://en.wikipedia.org/wiki/Lattice_field_theory

It turns out that Yang-Mills theory is important in most quantum gravity schemes.

Page 15 of Lee Smolin's exhaustive review of the state of the field found here: http://search.arxiv.org:8081/paper.jsp?p=hep-th/0303185&qid=1113796894988-1959050228 (link is to the abstract, but you can click through to the full text)

notes that both String Theory and LQG model gravity as non-abelian gauge theories. This ties in directly to the paper I note above, and Smolin also, a page or two later, explains that Yang-Mills is a core assumption of string theory approaches to quantum gravity.

The abstract of Smolin's paper is as follows:

Date (v1): Thu, 20 Mar 2003 18:32:29 GMT (88kb)
Date (revised v2): Fri, 11 Apr 2003 02:53:05 GMT (94kb)

How far are we from the quantum theory of gravity?
Authors: Lee Smolin
Comments: 84pages, one figure. Comments welcome. This is a review and it will be updated from time to time

An assessment is offered of the progress that the major approaches to quantum gravity have made towards the goal of constructing a complete and satisfactory theory. The emphasis is on loop quantum gravity and string theory, although other approaches are discussed, including dynamical triangulation models (euclidean and lorentzian) regge calculus models, causal sets, twistor theory, non-commutative geometry and models based on analogies to condensed matter systems. We proceed by listing the questions the theories are expected to be able to answer. We then compile two lists: the first details the actual results so far achieved in each theory, while the second lists conjectures which remain open. By comparing them we can evaluate how far each theory has progressed, and what must still be done before each theory can be considered a satisfactory quantum theory of gravity. We find there has been impressive recent progress on several fronts. At the same time, important issues about loop quantum gravity are so far unresolved, as are key conjectures of string theory. However, there is a reasonable expectation that experimental tests of lorentz invariance at Planck scales may in the near future make it possible to rule out one or more candidate quantum theories of gravity.

Again, just to show that the connection is pretty fundamental in the minds of the main LQG folks, here is a link where John Baez is talking about Yang-Mills theory in connection with quantum gravity (http://www.lns.cornell.edu/spr/2001-07/msg0033863.html), even though the discussion itself is pretty technical.

Wikipedia is a good jumping off point for getting to understand QCD. The main entry on QCD is here: http://en.wikipedia.org/wiki/Quantum_chromodynamics

 

[Kea]

...and the PF discussion on this problem:

https://www.physicsforums.com/showthread.php?t=38964&highlight=mass+gap

 

[wolram]

From the perspective of a totaly non scientist this theory seems to
boil down to three controversial points.

! does the Higgs field exist
2 does the Axion exist
3 is there a Mass gap

There seems to be plenty of discussion for and against all three, as i am
not at any seat of learning may be my picture is fuzzy, so how far up
the theoretical tree of reality are these three?

 

[marcus]

Hi ohwilleke,

I think in your post #20 here, which is what caught my attention, that by "larger program" you had something else in mind besides the fact that LQG was constructed (circa 1990) to be a non-abelian gauge theory.

...The single most important thing to understand about this paper is that it is part of a larger program of theoretical research to unify QCD and a loop quantum gravity verson of quantum gravity in much the same way that the electro-magnetic force and the weak force have been unified already...

But in your post #32 of yesterday evening you cite Smolin's 2003 survey "How far are we from the quantum theory of gravity" to illustrate.

LQG has always been formally analogous to other generalized Yang-Mills theories and I suppose Ashtekar had the analogy in mind in 1986 when he formulated GR with the connection as variable. Probably Rovelli and Smolin had the analogy very clearly in mind in the early 1990s when they first constructed LQG using Ashtekar variables.

Perhaps, now that you mention it, I can see this as the start of "a larger program to unify QCD and LQG".

But in the past I have tended rather to take the mathematical analogy for granted. Although there was a formal similarity, it did not seem to have led to an actual unified treatment of matter and spacetime geometry.

As I saw it, the matter was treated as a gauge field theory (on the one hand, and on the other) the geometry was treated similarly, but that formal similarity didnt actually unify the two. though it be wished devoutly that it would.

What I would like you to try to delineate if you can is what you see that's new.
What is going on this year that brings the goal closer of unifying matter with quantum spacetime geometry?
Can you relate your vision of a larger program to, for instance, the
paper by Freidel and Starodubtsev (which Stephon Alexander cites IIRC and which has John Baez so excited), or to some other recent work?

I'd be interested to have a better idea of how you see things.