Friday, May 05, 2006

Lubos Motl and Waldyr Rodrigues on Roger Penrose's skepticism about string theory

On May 5, 2006, at 4:54 PM, Waldyr A. Rodrigues Jr. wrote:

Dear Jack,

Without saying that string theory is wrong (or not even wrong) it is necessary to recall here that sometimes a lot of people may be completely wrong. As a good example, recall that during the period 1903-1906 some 120 trained scientists published almost 300 papers on the origins and characteristics of a totally spurious radiation first purported by a French scientist, René Blondlot. The amazing history of the N-rays affair is presented in: A. K. Dewdney, Yes, We Have No Neutrons, J. Wiley &Sons Inc., New York, 1997.

Also, how many papers have been written on the heat fluid of Becher before the advent of the kinetic theory of gases? I note that the heat fluid theory made many predictions...

Best regards,


P. S.: I like Clifford, spinors and superfield bundles,and of course supersymmetry, string theory, etc. By the way I just wrote a review for Math. Rev. on V. S. Varadarajan book: Supersymmetry for Mathematicians: An Introduction. However, I am very skeptical about the validity of string theory as a description of any physical world.
So is Roger Penrose. Well we cannot settle this here and now. Food for thought. :-)

On May 5, 2006, at 5:20 PM, Lubos Motl wrote:

On Fri, 5 May 2006, Jack Sarfatti wrote:

The ambiguity is in "string" here. The QCD flux tubes are not 9 + 1 superstrings, right? The issue here is the extra-dimensions and the supersymmetry for QCD.

Yes and no. The QCD flux tubes are conventionally thought of as tubes in 3+1 dimensions but they can also be indistinguishable from strings in 9+1 dimensions. For example, if the extra 6 dimensions are small, you won't see the details. But smallness is not the way how the 6 dimensions are hidden in AdS/QCD. In the N=4 gauge theory example, five of the dimensions span a sphere that is small for a small number of colors - but becomes huge and visible for a large number of colors.

More importantly, another (sixth) spatial coordinate - the holographic one - appears by the holographic tricks. You can think about the position in the new dimension (the distance from the boundary of the anti de Sitter space) to be equal to the energy scale of objects.

OK, Susskind I think discusses this in his little book.

Things with high energy (high frequency) are localized near the boundary of the AdS space; things with low frequency are localized far from the boundary, near the center of the AdS space. That's similar how a new 3rd dimension is encoded in real holograms in optics - although not identical - which is why we also talk about holography: places on the hologram where the interference pattern is denser are closer to the screen (or further? who cares).

Let me say an example that is not quite accurate but it conveys the flavor of the answer. A flux tube in 3+1 dimensions can carry various local excitations - kinds of "phonons" that propagate along the flux tube. Again, something that you can extract from the gauge theory if you look carefully.

If you look at the possible kinds of phonons that a real flux tube in 3+1 dimensions can carry, you will find, among a few other things I want to neglect, six scalar excitations. They are effectively described by 6 scalar fields defined on the flux tube. These 6 scalar fields know about the position of a given point on the flux tube in 6 additional dimensions. This means that the strings live in 9+1 dimensions, and by ignoring the internal dynamics of the flux tubes (and only focusing on the geometric shape), you are also overlooking the extra 6 dimensions.

OK - I like those 6 scalar fields of course, I have them in my
from a naive POV of course.

In string theory, it is very typical that there are several exactly equivalent descriptions of the same system, and many things that look like "non-geometric" "kind-of-matter" objects on one side have a completely pure geometrical description on the other side, and vice versa. Space is emergent: there is no universally valid method to determine which information about physics is geometric (about position) and which is internal (about the internal features of the objects). These two groups of characteristics of objects and fields in string theory can be equivalent, while one of them may be more useful and "weakly coupled" in one limit of the parameter space than the other one.

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On May 5, 2006, at 5:02 PM, Jack Sarfatti wrote:

On May 5, 2006, at 4:41 PM, Lubos Motl wrote:
On Fri, 5 May 2006, Jack Sarfatti wrote:

Now, wait. What are you saying? Are you saying Wilczek cannot derive confinement with flux tubes in 3 + 1 space-time but needs to invoke 9 + 1 space-time with supersymmetry and branes and the ADS/CFT et-al?

No. I am saying that the string theory approach gives us new ways to understand why confinement is there and how things behave in the real QCD of Wilczek et al. SU(3) gauge theory is however perfectly enough to study all strongly interacting physics, at least in principle - if one has powerful enough computers.

The dual string theory is an alternative approach to the same problem. However, this investigation focuses on a different aspect of string theory than the main goal for which string theory is studied: the string theory relevant for QCD is a string theory in a highly curved background. Conventionally, we use string theory to understand four-dimensional interactions including four-dimensional gravity. However, the first (QCD)
picture is a part (limit) of the second picture in many particular realizations of the real world within string theory.

I mean, are you saying that plain vanilla Yang-Mills SU(3) point particle QCD in 3 + 1 is incomplete and cannot within itself get quark confinement and asymptotic freedom? Is that what you mean?

No, this is not what I mean. In this setup, string theory is just a mathematical tool to calculate things that are difficult to calculate with normal methods of QCD. Two quarks of different color can't be infinitely separated because there is a string in between them that tries to shrink them. The whole theory can be defined with these strings as the fundamental objects, instead of the gluons.

The ambiguity is in "string" here. The QCD flux tubes are not 9 + 1 superstrings, right? The issue here is the extra-dimensions and the supersymmetry for QCD.

Gauge theory is exactly equivalent to physics of strings

That's interesting. Do you mean local gauge theory, i.e. Yang-Mills in 3 + 1 is equivalent to a 9 + 1 string/brane theory with supersymmetry and holography in the form of ADS/CFT?

Yes, in this case you are right on the money. The AdS/CFT correspondence, in its most popular form, is saying exactly this. An SU(N) Yang-Mills theory in 3+1 dimensions is exactly equivalent to a 9+1-dimensional string theory with supersymmetry, branes, and everything else. The gauge theory description is simpler and more convergent if the `t Hooft coupling, lambda = g_{Yang-Mills}^2 * N, is small.

OK, that's interesting. Thanks.

The string theory description is more natural, weakly coupled, and more convergent if lambda is large: in this limit, the physics of the d=4 gauge theory indeed develops ten spacetime dimensions that are almost flat. Five of them are compact - they span a sphere whose radius grows with a positive power of lambda. Five of them organize themselves into anti de Sitter space, a curved spacetime whose boundary at infinity is four-dimensional - this is where the gauge theory was originally defined.


Maldacena and its 3900+ references mentioned previously

You can also find this 250+ page-long review useful:

OK thanks.

Is that a theorem by Witten?

It's normally called the Maldacena correspondence, but because Witten has made it really famous, you can also call it a theorem by Witten. See his paper

plus its 2700+ citations.

and extra dimensions are necessary for the picture to work.

What is the best pedagogical review of that?

Not sure whether I gave you the best one, but one review is listed above. Dozens of other reviews are listed in section VI (gauge-gravity duality) on page 8 of the resource letter by Marolf

Whenever my blog covers a topic, it's of course the most pedagogical source. ;-)

This appears to be the model Penrose seems to debunk in The Road to Reality.


Let me remind you that type IIB string theory requires 10 spacetime dimensions.

Why 10? Can it be because the Poincare and the deSitter groups have 10 parameters?

Unlikely. String theory requires ten dimensions to cancel the conformal anomaly on the worldsheet. In the RNS formalism, there must be superpartner fermions for each boson (spacetime direction). Each fermion contributes 1/2 of the anomaly of the corresponding boson. Together, they have 3D/2 of units of anomaly. Then the supersymmetric RNS worldsheet also requires bc ghosts and beta-gamma ghosts. The bc ghosts contribute 1-3.3^2 = -26 units of anomaly; the beta-gamma ghosts contribute -1+3.2^2 = 11 units of anomaly. Together, bc and beta gamma have -26+11 = -15, which is canceled against 3/2 times 10 dimensions. There are other ways to derive the number but all of them require at least some technology. The number 10 has probably nothing to do with the number of your fingers, digits, or generators of the Lorentz group in d=4.

Detailed physics of interacting strings and extra dimensions can be seen in N=4 d=4 gauge theory as long as the number of colors N is large.

How can N = 4 and N large hold at the same time?

It's a different N. When I wrote N=4, I mean scriptN=4, which counts the number of supercharges. The other N that should be large is the number of colors - something equal to "3" in real QCD.

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