## Friday, June 04, 2010 ... //

### Asymptotic darkness vs safety and non-heterotic F-theory

F-theory models without heterotic crutches

I will mention two hep-th preprints today. The first one is

A Note on G-Fluxes for F-theory Model Building.
Joe Marsano, Natalia Saulina, and Sakura Schafer-Nameki start with a nice explanation of the role of the heterotic duals in F-theory model building. The GUT group in F-theory models is localized near singular cycles where K3-like singularities develop.

They can be locally dualized to a heterotic description: recall that F-theory on a K3 is equivalent to heterotic strings on a T2 and this duality may be applied fiber-wise over the four-real-dimensional geometry of the cycle that supports the singularity. The heterotic description doesn't see that the K3-fibration is actually not global so the heterotic optics is OK for all the physics of the model based on gauge theory - but not for the full model including gravity.

Consequently, heterotic methods have been used in F-theory model building, especially in the case of the G-fluxes. However, the importance of the heterotic tools is partly of sociological or historical nature: people have been trained to use them so they use them now, too. The heterotic optics has also led to some early confusion about the existence of models because some people were assuming that the local, heterotic description was globally equivalent to the F-theory, even when it came to constraints. Of course, the origin of these early confusions has been understood by the experts.

The authors of this new preprint start to develop tools to deduce various aspects of physics, such as the chirality of matter fields, that use intrinsically F-theoretical methods and that don't rely on the heterotic crutches.

Do they reconcile asymptotic safety with black hole physics?

Sayandeb Basu and David Mattingly chose a pretty long title for their preprint:
Asymptotic Safety, Asymptotic Darkness, and the hoop conjecture in the extreme UV
They acknowledged my arguments about the incompatibility of the asymptotic safety and asymptotic darkness.

At very high center-of-mass energies, the spectrum of a quantum gravitating theory should be dominated by black holes whose entropy only grows with the area. However, asymptotic safety claims that the very-high energy limiting dynamics of gravity is a conformal field theory whose entropy should grow with the volume. That's incompatible with the first sentence of this paragraph.

Because the black holes are the final states of a gravitational collapse, because the entropy has to grow, because the black hole entropy is so small (relatively to the volume), and because the collapse of any other sufficiently massive and small configuration to a black hole is inevitable due to the hoop theorem, there's no room for the hypothesized excessively numerous high-entropy CFT states: the asymptotic safety can't work. It's as simple as that.

The authors try to find some loopholes but as far as I can see, they don't really understand or state the argument in its entirety.

So they only focus on one aspect, the hoop conjecture. In 1972, Kip Thorne conjectured that a sufficiently dense chunk of matter that can be encircled by a "hoop" of length 2.pi times the Schwarzschild radius calculated from the object's mass will inevitably collapse to the black hole.

On Tuesday, Kip Thorne celebrated his 70th birthday. Congratulations! The authors prepared a special gift for him, too. They claim that the most important application of Thorne's theorem is bullshit. ;-)

The arguably most important application of the theorem is in quantum gravity because the theorem prevents us from seeing sub-Planckian distances. Attempts to see "them" will produce a black hole that will destroy the audacious experimenters and prevent them from publishing their findings. :-) In a physical sense, the ultrashort distances don't exist.

Now, the authors claim that Thorne's proof may be circumvented when the higher-order corrections are added. The black hole may form but doesn't have to - it's up to the coefficients of the higher-order terms, they say. Strangely enough, they also say at the end of their article that an "enshrouding horizon" has to develop around a lab that tries to measure the sub-Planckian effects, anyway. But the horizon is what defines the black hole, isn't it? So it does form, doesn't it?

Well, if they're talking about some physics that occurs near the very singularity, a very small region immersed in a much larger black hole, I have no serious problem with that even though it may be wrong, too. But it would still be true that the black hole dominate the high-mass spectrum and the CFT can't be valid in the bulk of the space.

So I don't understand the very logic of this claim but even if it makes sense, it is extremely limited in its reach because they don't actually say whether the CFT high-mass states predicted by safety exist, whether their entropy/number may exceed the black hole bounds, and whether they can ever collapse to the black hole. And if they don't, why it doesn't violate relativity and locality at arbitrarily long distances and why it doesn't violate the second law.

Consequently, I don't think that they have eliminated the contradiction between the asymptotic darkness and safety. They have only questioned a very incompletely stated proof of the inconsistency and attacked one piece of it by a foggy argument based on some questionable formalism.

Much more generally, I don't understand the point of papers of this kind. Some people try to claim that some no-go theorems don't necessarily work - by some arguments that look rhetorical rather than specific. That would be fine but they just don't offer any "tangible" counter-examples or explanations how the stuff works in their opinion.

It's like protesting against the Coleman-Mandula theorem without having any hint of supersymmetry etc. I don't know what's the point of such complaints - and I think that they're wrong, even though it is often hard to show that some foggy criticism is wrong.

If they want to claim that there's an alternative to the sensible statement that the entropy bounds hold and that the entropy in a given region can't exceed the black hole entropy, a statement that is supported by a big consistent informal picture as well as all the diverse and detailed descriptions of the stringy vacua we know, they should offer a conceivable replacement for all "components" of the lore they want to erase.

The statement of the type "we can imagine that step XY in a theorem could be circumvented because we don't understand why it's not and we may add some random terms to the equation" is just not enough if the authors of the theorem did a much more detailed job in showing why the step is actually likely to be right. If you add a new term in an equation, it's your duty to check that the term remains compatible with all other physical phenomena where the previous equation without the term has been checked.

Well, it's almost certainly not in this case and in similar cases.