# Alexander paper - CP and lambda

1. Mar 27, 2005

### 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."

2. Mar 27, 2005

### 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

3. Mar 27, 2005

Staff Emeritus
$B \wedge F$ 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.

4. Mar 27, 2005

### nightcleaner

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. Lets 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:

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

Last edited by a moderator: Mar 27, 2005
5. Mar 27, 2005

### marcus

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 lets get back on topic, what is this paper about, in layman's terms, if anyone would like to take the trouble to tell us?

Last edited: Mar 27, 2005
6. Mar 27, 2005

Staff Emeritus
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.

7. Mar 27, 2005

Staff Emeritus
Here's the money graf from the paper

Anybody want to discuss it?

8. Mar 27, 2005

### marcus

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]

Last edited: Mar 27, 2005
9. Mar 27, 2005

### 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 [Broken]
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."

Last edited by a moderator: May 2, 2017
10. Mar 27, 2005

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

11. Mar 27, 2005

### marcus

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.

Last edited: Mar 27, 2005
12. Mar 27, 2005

### 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.

13. Mar 27, 2005

### 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.

14. Mar 27, 2005

### Chronos

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

Last edited: Mar 27, 2005
15. Mar 27, 2005

### marcus

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

16. Apr 13, 2005

### marcus

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:

Last edited: Apr 13, 2005
17. Apr 14, 2005

### 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).

18. Apr 14, 2005

### ohwilleke

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

19. Apr 14, 2005

### marcus

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

http://arxiv.org/hep-th/0503146 [Broken]

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---

Last edited by a moderator: May 2, 2017
20. Apr 14, 2005

### 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.

Last edited: Apr 14, 2005