The model that Lisa Randall and Raman Sundrum propose consists of two four dimensional (Minkowskian) branes, bounding a five dimensional bulk between them. In their initial model the branes are very close together; this is not a "large extra dimensions" model. The motivation of the model is to explain the hierarchy problem. One of the branes is called the Weakbrane; it is the home of the particles of the standard model and their interactions. The other brane is the Gravitybrane and on it are defined the bosonic (non-supersymmetric) string theory gravitons; each of them is a vibration mode of a closed bosonic string. Each brane is at a characteristic energy, the Weakbrane as its name indicates is at the Weak energy scale, around a TEV, and the Gravitybrane is at the much higher string energy scale. The graviton, in traditional Randall-Sundrum fashion, can leave its brane and roam the five dimensional bulk space between the branes, Now in Einstein's physics, energy curves geometry, and both of these branes carry energy, so the geometry of the bulk between them is curved. This can be calculated from Einstein's equations in five dimensions. Randall in her book characterizes this curvature as the kind technically known as a warp. This means that sections taken within the bulk but parallel to the branes have the same geometry as the branes (i.e. "flat" Minkowskian), but differ by a scale factor, again having the technical name "warp factor" (hello Mr. Spock!). The definition of size actually differs from section to section! (hello, Alice in Wonderland!). The effect of the curved geometry is to alter the probabiity of finding a graviton (from distortion of its wave function); it is high near the Gravitybrane and low near the Weakbrane. I want to emphasize that this behavior is all deduced from the specification of the model; the curvature is calculated from Einstein's equations applied to the known brane energy, and the graviton wave function is calculated within the curvature. This graviton behavior provides the explanation of the hierarchy problem. From the book Warped Passages page 393: There is another consequence of the warp scaling in the bulk: from page 398: After Randall and Sundrum published this model, physicist Alex Pomerol suggested that it could account for the unification of the forces at high energies as well as the hierarchy problem. In Pomerol's version of the model the particles of the standard model travel through the bulk, and he shows the high energy behavior of the forces converge. He uses supersymmetry (as in the older Randall-Sundrum model) to address the hierarchy problem. But Randall shows you can get both unification and hierarchy without any supersymmetry if you only restrict the Higgs boson to the Weakbrane and let all the other standard model particles wander the bulk. Now in particuar note the graviton. Each graviton in the five dimensional bulk will have a five-momentum, and some of them will have five-momenta that have zero component orthogonal to the fifth dimension. The wave function of such a particle will have four-components in the Weakbrane that will have zero three-momentum and will therefore appear there as mass. So an interacting particle with mass about the TEV scale of Weakbrane physics is predicted to be detectable at the LHC. But there's more. The momentum of the graviton can have a quantized spactrum coming from vibration modes of the closed string as wound some number of times around the topology of the compacted manifolds. So these LHC particles will have a very characteristic mass spectrum of TEV, 2TEV, 3TEV, and so on. She can also calculate that unlike the free graviton, these particles are not as suppressed by the curved geometry; their interaction probability is 16 orders of magnitude higher than the free graviton (p. 408). How will the physics of these particle appear at LHC? On page 409 of her book Randall shows a (pop) Feynmann diagram: two protons collide and a quark interacts with an antiquark at the TEV energy scale producing one of these particles (along with jets of other particles), which then decays into something else, in her diagram an electron and a positron. The key here is the energy spectrum of the interaction; it should show the characteristic TEV, 2TEV, 3TEV, etc. pattern. Also all these particles will inherit spin 2 from the graviton and that will be an earmark. So an early show up might be the lowest level of them, about a TEV of energy and spin 2. Notice that although Randall likes to distinguish herself from some of the more fancy-dan string thorists, her whole model is built out of basic string theory. So it's not really true to say that "string theory predicts nothing", this little piece of it predicts explixit observable physics. And this model, at least is eminently falsifiable.
that's good. So Randall-Sundrum have a specific stringy model that IS testable. and is falsifiable by having the particles it predicts NOT be observed at LHC. I assume this is not only explained in her book. they must have published it, there must be a raft of papers, I'd guess. Eventually we will get some links. I have been hearing about Randall-Sundrum models for quite a while. I am very glad that there is this one that is on record as predicting LHC observable particles.
:rofl: Marcus, that's too funny! These predictions are YEARS old. See eg. Warped Phenomenology http://lanl.arxiv.org/abs/hep-ph/9909255 Authors: H. Davoudiasl, J.L. Hewett, T.G. Rizzo Journal-ref: Phys.Rev.Lett. 84 (2000) 2080 We explore the phenomenology associated with the recently proposed localized gravity model of Randall and Sundrum where gravity propagates in a 5-dimensional non-factorizable geometry and generates the 4-dimensional weak-Planck scale hierarchy by an exponential function of the compactification radius, called a warp factor. The Kaluza-Klein tower of gravitons which emerge in this scenario have strikingly different properties than in the factorizable case with large extra dimensions. We derive the form of the graviton tower interactions with the Standard Model fields and examine their direct production in Drell-Yan and dijet events at the Tevatron and LHC as well as the KK spectrum line-shape at high-energy linear \epem colliders. In the case where the first KK excitation is observed, we outline the procedure to uniquely determine the parameters of this scenario. We also investigate the effect of KK tower exchanges in contact interaction searches. We find that present experiments can place meaningful constraints on the parameters of this model.
so (according to what you say) what selfAdjoint was talking about by way of predictions that would falsify some model and what Lisa Randall was talking about in her book is represented in some sense by this 1999 paper http://arxiv.org/hep-ph/9909255 I see JoAnne Hewett, one of the group bloggers at Cosmic Variance is a co-author, as is Thomas Rizzo. Thanks for the link. I was hoping someone (in fact EXPECTING someone) to provide a link to something representative of what Randall and selfAdjoint were talking about, for those of us who dont own the book and like stuff to be online. I do not find in the paper a clear statement of what theory will be falsified if what definite things are observed, or fail to be observed. But perhaps that will eventually be made explicit. I do not know for sure that this paper actually is representative of what selfAdjoint was talking about, and what Randall was discussing in her recent book. A lot has happened since 1999, I imagine and the situation may have altered. But selfAdjoint can confirm it if this is a representative link. What Hewett et al say at the conclusion, right at the end of their paper, is We find the scenario of gravity localization to be theoretically very attractive, and even more importantly, to have distinctive experimental tests. We hope that future experiment will eventually reveal the existence of higher dimensional spacetime... (that seems to be a general focus of concern for them---hopes for evidence of extra dimension) I would be curious to know if the people running LHC are actually going to be worrying a lot about testing such and such a vintage 1999 Randall-Sundrum model! A Randall-Sundrum model is not string theory exactly, but it is something you can test So maybe they will! BTW Sabine, do you have some links to old papers that overlap with Distler's recent proposal of a way to make string theory falsifiable? Any thoughts on that. What Distler ADVERTISES at least seems considerably more interesting than testing some particular R-S model. Because, if we accept what he says, more is at stake. It is presumably more generic.
Actually two of the authors of the 1999 article Sabine mentioned have since then proposed what I think is a BETTER TEST http://www.physorg.com/news10682.html Nice smile. It is actually a test of Loop Quantum Gravity, however, because it attempts to see whether or not there are extra dimensions by looking for microscopic black holes at LHC. the discovery of extra dimensions would refute Loop-and-allied QG developed to date because development has concentrated on the observed 4D world. Nevertheless Hewett seems to be a very nice person and she is presenting her proposal about micro black holes at LHC as a test of STRING THEORY. Perhaps we should look on this with a measure of indulgence given the media and intellectual climate. but I don't see how NOT finding extra dimensions at LHC would falsify string theory. ====================== MORAL OF STORY JoAnne Hewett at SLAC/Stanford is a Phenomenology person to watch. She is an establishment insider, sits on important funding policy committees (recently showed up at Peter Woit's blog and he congratulated her on a report to congress) And furthermore she authored a R-S phenomenology paper in 1999 (that Sabine cited) and proposed what she offers as a STRING phenomenology test in 2006. And it was that micro black hole thing that Steven Giddings was writing about in the Sci Am. Signs are she's a leader in phenomenology. ================== apologies to those who know all this already. Ive never been much interested in anything that needs extra dimensions----since the 4D models are making rapid progress there's never seemed to be a need. So I am just beginning to form an idea of what people like JoAnne Hewett are up to.
That doesn't mean its not possible. I don't see why LQG shouldn't equally well describe extra-dimensions (in the easiest case they are flat). I think you refer to a paper of hers that is titled something like 'testing critical string theory' or so. She points out that there is a way to falsify string theory. That is to find MORE than 11 dimensions. And says, well, in principle we could do so at the LHC with the micro black holes. I don't agree on the analysis in the paper, and I find it a very unlikely thing to happen, but she has a point there, and it's a cute idea. Best, B.
that is right, what a good memory you have! I was just talking about that paper in another thread, it is http://arxiv.org/abs/hep-ph/0503178 Black holes in many dimensions at the LHC: testing critical string theory JoAnne L. Hewett, Ben Lillie, Thomas G. Rizzo 5 pages, 4 figures. Phys.Rev.Lett. 95 (2005) 261603
Since it is a popular topic, what you can test at LHC, I want to re-iterate my view so as to make it very clear. Hewett's proposed test is a test of NON-STRING QUANTUM GRAVITY Because the approaches to QG that have been developed (like spinfoams, group field theory, dynamical triangulations, LQG) predict that you DO NOT SEE EVIDENCE OF EXTRA DIMENSIONS. If you SEE extra dimensions this disfavors LQG and allied nonstring gravity. So it is these non-string QG theories that are thereby falsifiable. ============== On the other hand Randall-Sundrum DOES NOT PREDICT ANYTHING about whether you see or dont see. If you see evidence of extra dimension, then fine. But also if you DONT see evidence, that is fine too because maybe the energy was not high enough to detect them. ============== Several of the non-string QGs also predict energy dependence of the speed of light on a scale observable by the GLAST satellite (see http://uk.arxiv.org/abs/hep-th/0605052 ) GLAST is scheduled for launch in 2007-----so it is yet another near-term test of non-string QG predictions. They predict an order-one dispersion coefficient with dispersion suppressed at Planck scale. That is, they say that this effect should be observed in Gammaray Bursts and at at energies which GLAST will detect. Several theories would be in serious trouble if either evidence of extra dimensions is observed or else the predicted variation in speed of light is not observed. So I'd say there are Two major tests of non-string QG coming up in the near term.
This MSNBC news story today mentions several new suggestions to test the Randall-Sundrum model, including an application of GLAST described in this recent paper. Charles R. Keeton and A.O. Petters
Is it possible that helical strings as [complex] harmonic oscillators could accommodate both the Randall 'large' and Arkani-Hamed 'small' concepts of curled-up, unseen dimensions? A helix is certainly coiled and applies to QM via the 3D Schroedinger wave equation and a 'space double helix' [likely EM related] was imaged near the galactic core. Helices [or helicoids] may as [complex] harmonic oscillators may even satisfy the search for the fifth dimension or the helical properties attributed to the 11th dimension of U-duality in M-theory. A cylindrical space-time [or because of eccentricity an ellipto-cylndrical] complex 5D space may even satisfy the t'Hooft epislon concept of nD as (n-1).99999D. Helices [with virtual volumes] as [complex] harmonic oscillators may even have gauge-corresponding loops [with virtual areas] of the same period.
Is it possible that helical strings as [complex] harmonic oscillators could accommodate both the Randall 'large' and Arkani-Hamed 'small' concepts of curled-up, unseen dimensions? A helix is certainly coiled and applies to QM via the 3D Schroedinger wave equation and a 'space double helix' [likely EM related] was imaged near the galactic core. Helices [or helicoids] may as [complex] harmonic oscillators may even satisfy the search for the fifth dimension or the helical properties attributed to the 11th dimension of U-duality in M-theory. A cylindrical space-time [or because of eccentricity an ellipto-cylndrical] complex 5D space may even satisfy the t'Hooft epislon concept of nD as (n-1).99999D. Helices [with virtual volumes] as [complex] harmonic oscillators may even have gauge-corresponding loops [with virtual areas] of the same period.