Monday, October 17, 2011

Super Extra Loop Quantum Gravity

In the summer, I noted a recent paper that scored remarkably low on the bullshit index:
    Towards Loop Quantum Supergravity (LQSG)
    Norbert Bodendorfer, Thomas Thiemann, Andreas Thurn

    Bullshit Index : 0.08
    Your text shows no or marginal indications of 'bullshit'-English.

But what is the paper actually about? It is an attempt to make contact between Loop Quantum Gravity (LQG) and Superstring Theory (ST). Both are approaches to a quantization of gravity, one of the big open problems in theoretical physics. LQG directly attacks the problem by a careful selection of variables and quantization procedure. String theory does not only aim at quantizing gravity, but at the same time at unifying also the other 3 interactions of the standard model by taking as fundamental the strings that give it its name. If quantizing gravity and unifying the standard model interactions are actually related problems, then string theorists are wise to attack them together. Yet, we don't know if they are related. In any case, it has turned out that gravity is necessarily contained in ST.

Both theories still struggle to reproduce general relativity and/or the standard model, and to make contact to phenomenology, though for very different reasons. This begs the question how the theories compare to each other, whether they give the same results for selected problems. Unfortunately, so far this has not been possible to answer because LQG has been developed for a 3+1 dimensional space-time, while ST famously or infamously, depending on your perspective, necessitates 6 additional dimensions that then have to be compactified. ST is also, as the name says, supersymmetric. It should be noted that these both features, supersymmetry and extra dimensions, are not optional but mandatory for ST to make sense.

I've always wondered why one hasn't extended LQG to higher dimensions since the idea of extra dimensions is appealing and somebody in the field who should have known better once told me it would be straight forward to do. It is however not so because one of the variables (a certain SU(2) Yang-Mills connection) used in the quantization procedure relies on a property (the equivalence of the fundamental and adjoint representations of SU(2)) that is fulfilled only in 3 spatial dimensions. So it took many years and two brilliant young students, Norbert Bodendorfer and Andreas Thurn, to come up with a variable that could be used in an arbitrary number of dimensions and to work through the maths which, as you can imagine, didn't get easier. It required to work around the difficulty that SO(1,D) is not compact and digging out a technique for gauge unfixing, a procedure that I had never heard of before.

Compared to the difficulty of adding dimensions, going supersymmetric can be done by simply generalizing the appropriate matter content which is contained in the supergravity actions, and constructing a supersymmetry constraint operator.

Taken together, this in principle allows one to compare the super extra loop quantized gravity to string theory, to which supergravity is a low energy approximation, though concrete calculations have yet to follow. One of the tasks on the to-do list the entropy of extremal supersymmetric black holes to see if LQG reproduces the ST results. (Or if not, which might be even more interesting.) Since LQG is a manifestly non perturbative approach, this relation to string theory might also help filling in some blanks in the AdS/CFT correspondence in areas where neither side of the duality is weakly coupled.

25 comments:

Thomas Larsson said...

Meanwhile at Cern, the LHC is working hard to rule out supersymmetry.

And here in Stockholm, this years Nobel prize goes to the discovery that AdS is unphysical.

Bee said...

Hi Thomas,

Yes... Clearly that would have been more interesting 10 years ago... I suspect the scale of SUSY breaking will just silently be moved out of LHC reach. In any case, there's no denying that ST and LQG are the most widely pursued approaches to QG, so it's good trying to make contact. Best,

B.

A. Mikovic said...

Dear Bee,
I have a couple of comments regarding your post about loop supergravity. You said
"Both theories still struggle to reproduce general relativity and/or the standard model", which is not completely correct. Namely, there hes been a recent breakthrough on determining the semiclassical limit of LQG, which is using the effective action approach, see, arXiv:1104.1384 (Effective action and semiclassical limit of spin foam models, by A. Mikovic and M. Vojinovic) to appear in Class. Quant. Grav. (2011). There it was shown that a simple modification of the EPRL/FK spin-foam vertex amplitude gives a spin foam
model whose semiclassical effective action is the Einstein-Hilbert one plus small corrections.

As far as the goal of relating the string theory to LQG, the way to do it is to formulate GR on a loop manifold, something that was tried in the early days of string theory, but it was not developed because of the lack of the appropriate mathematical formalism.

Regards,

Aleksandar Mikovic

Bee said...

Hi Aleksandar,

Thanks for your interesting comment. Best,

B.

Arun said...

Thanks, Bee, this is interesting!

Plato said...

Bee:If quantizing gravity and unifying the standard model interactions are actually related problems, then string theorists are wise to attack them together. Yet, we don't know if they are related. In any case, it has turned out that gravity is necessarily contained in ST.

The benefit of asking a question is dominating how we push back perspective about the beginning of, and the formation of the universe. At least this is how I see what has happened. So have we been successful? I think we have so far.

Once you recognize this, then the idea seems more correlative to what and how you see the experiments in relation to how they can help with understanding the universe. The ole woodcut holds some value then as to the depth of how we are looking at structure.

Best,

kneemo said...

Hi Bee

Nice post. Back in 2000, Smolin proposed a supersymmetric and quantum deformed SU(16) extension of LQG and suggested it was dual to the IKKT and dWHN-BFSS matrix models for M-theory (hep-th/0006137).

Plato said...

Bee,

Here is a String Theory Crib Sheet for those interested in exploring the "Deep Structure of the Universe."

Best,

Uncle Al said...

http://arxiv.org/abs/1107.2917
"Chiral Scale and Conformal Invariance in 2D Quantum Field Theory"
Phys. Rev. Lett 107 161601 (2011)

Postulated vacuum mirror symmetry toward mass, elegant supersymmetry, has ever-growing empirical failures and theoretic dissent. If string theory is discredited in kind, one sighs relief. Test for an empirical trace vacuum chiral background toward mass.

Epicycles have no deficiencies in rigor or goodness of fit, nor do Egyptian fractions. Still... go heliocentric and decimal.

Neil Bates said...

BTW, note that the "bullshit index" really measures style directly, not BS-i-ness which is only loosely correlated (in case I ever score highly on such ...)

Steven Colyer said...
This comment has been removed by the author.
Steven Colyer said...

Hi Bee,

What does Lee Smolin think about this paper?

What does Carlo Rovelli?

For that matter, what does Ed Witten ... but I think we know.

And before I go on, I second Neil's motion re the Blabla(BS)meter being about style not substance.

The first I heard of an attempted unification of Loops and SillyStrings was in one on Brian Greene's books. Brian is great, he's a peacemaker, not a confrontationalist. But whatever he is, what I remember is that at the time of publication, there is no reason Stringsies and Loops can't BOTH be true.

Nor can't they both be wrong. I think Brian talked to Lee to produce that passage, and I think it was Lee's idea. But I also remember reading that afterwards that Lee backed up. Possibly because diplomacy sometimes moves in only one direction, and the SUSYstringers were having none of meeting Loops at the time, or even acknowledging its existence. Elitist bleepers.

But in the final analysis, Strings are background-dependent and Loops background-independent.... or so they say.

And as far as uniting THOSE two differences ... good luck, folks.

Zephir said...

In context of AWT the relation of string theory to LQG can be understood easily with using of model of nested density fluctuations of supercritical fluid: the string theory focuses to individual fluctuations (strings, membranes), the LQG to the resulting foam. Apparently, both theories are biased from physical reality in dual way.

Robert L. Oldershaw said...

Untestable pseudo-reality prevails in Platonist circles regardless of contradictory physical evidence.

Why am I not surprised?

Bee said...

Neil, Steve,

Come on, I wrote explicitly: "[The Blablameter] does not check a text for actual content and is not able to judge the validity of arguments, it is merely a rough indicator for writing style." Best,

B.

Steven Colyer said...
This comment has been removed by the author.
Steven Colyer said...

Hi Bee,

I apologize, Bee. Neil and I know what you wrote, I apologize for not being more specific. Our problem with the blablameter is that it is in serious need of a tweaking, it's scaled too low. But enough about that! There's PHYSICS to be done!

I asked some serious questions. What are your responses? Is all I'm asking.

Best,
Steven

Bee said...

Hi Steve,

Okay, to reply to your serious questions: I don't know what Lee thinks, I'm not his spokesperson. Neither do I know what Carlo Rovelli, Ed Witten or Brian Greene think. Most of the time, I don't even know what I think. The issue of background independence in ST is subtle. Moshe Rozali wrote a good paper about it. I don't know if ST and LQG can both be true. Probably, concepts of both can be true, but I'm skeptical about the full-blown theories that have been developed so far. Best,

B.

Giotis said...

"I don't know if ST and LQG can both be true"

Well look how the concept of graviton emerges in the two theories. Completely different mechanisms; it's like comparing oranges and apples.

Steven Colyer said...

Thank you Bee and Giotis.

"Most of the time, I don't even know what I think."

So it's not just me? :-) I know what you mean. This speculative stuff can drive us looney if we think about it too much. But it's important.

One of the problems of reading books on this stuff is the authors themselves are entitled to change their minds, and you could be reading old news. For example, on quantum entanglement for example, I've read say ten different authors' takes on it, and there are something like 5 different interpretations of it. I sometimes wonder if the scientific elite talk to each other, but they must, look at all these conferences!

From Wikipedia:

Hendrik A. Lorentz was chairman of the first Solvay Conference held in Brussels in the autumn of 1911. The subject was Radiation and the Quanta. This conference looked at the problems of having two approaches, namely the classical physics and quantum theory. Albert Einstein was the second youngest physicist present (the youngest one was Lindemann). Other members of the Solvay Congress included such luminaries as Marie Skłodowska-Curie and Henri Poincaré.

So the 100th anniversary of the FIRST Physics conference is ... now? Anyone have an exact date?

Happy 100th Birthday, physicists! :-)

N said...

I really can not understand why you call ST (or LQG for that matter) a theory These are all but hypetheses, some even far from that.

;))n.

Bee said...

Hi N,

It is somewhat unfortunate that in the pop sci corners of the blogosphere there has been a trend to claim the word 'theory' for an experimentally verified theory, which is however not how scientists commonly use the word. It is more commonly used for a well-worked out consistent framework of a testable hypothesis. The aether theory was a theory. It just turned out not to describe reality. At least it could be falsified. (Up to some accuracy that is, which is why it's entered the stage of zombie-theories that come back to haunt us.) ST and LQG are in principle testable, and though at least so far they are not in practice testable they meet all criteria for theories in the scientific sense. Best,

B.

N said...

Thanks Bee for the answer. Back in 60/70ies when I went to school Popper was the law. Things do change and thanks god they do :)

N said...

Hi Bee,

I know this is O/T, but:

on another Physics Forum, I had a discussion concerning the OPERA experiment, and (Ill not go into details, but he was not Lee Smolin) we ended up with this:

Photons interact with physical particles and obey the curvature of space, then, would they not interact with virtual particles? Some of them coming to the target sooner, some later?

Then, what is the speed of light in vacuum? Is it an average? If so, the standard deviaton tells us that that some of the photons shall be slower, then some faster than c?

Or do you think that photons do not interact with virtual particles?

Well, after that my friend went silent---

And I still dont know what to think of it.

Sorry to bother you with this dillema, I believe that it is only a consequence of the fact that I do not know basics (which I know I dont).

:))n.

Bee said...

Hi N,

Yes, photons "interact" with virtual particles. All particles do. It leads to a renormalization of the propagator, but photons remain massless and continue to move with the invariant speed of special relativity, formerly known as the speed of light. Best,

B.