Testing string/m-theory extra dimensions prediction

[kodama]

String theory and M-theory and Kaluza Klein theories predicts additional extra dimensions

at least 2 recent papers proposed tests these predictions of extra dimensions

String theory phenomenology and quantum many body systems
Sergio Gutiérrez, Abel Camacho, Héctor Hernández
(Submitted on 24 Jul 2017)
The main idea in the present work is the definition of an experimental proposal for the detection of the number of extra{compact dimensions contained as a core feature in String Theory. This goal will be achieved as a consequence of the fact that the density of states of a bosonic gas does depend upon the number and geometry of the involved space{like dimensions. In particular our idea concerns the detection of the discontinuity of the specific heat at the condensation temperature as a function of the number of particles present in the gas. It will be shown that the corresponding function between these two variables defines a segment of a straight line whose slope depends upon the number of extra{compact dimensions. Resorting to some experiments in the detection of the specific heat of a rubidium condensate the feasibility of this proposal using this kind of atom is also analyzed.
Comments: 6 pages
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1707.07757 [gr-qc]

and

Signatures of extra dimensions in gravitational waves
David Andriot, Gustavo Lucena Gómez
(Submitted on 24 Apr 2017 (v1), last revised 21 Jun 2017 (this version, v2))
Considering gravitational waves propagating on the most general 4+N-dimensional space-time, we investigate the effects due to the N extra dimensions on the four-dimensional waves. All wave equations are derived in general and discussed. On Minkowski4 times an arbitrary Ricci-flat compact manifold, we find: a massless wave with an additional polarization, the breathing mode, and extra waves with high frequencies fixed by Kaluza-Klein masses. We discuss whether these two effects could be observed.
Comments: v1: 21 pages + appendices, comments welcome! v2: few minor additions
Subjects: High Energy Physics - Theory (hep-th); Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Astrophysical Phenomena (astro-ph.HE); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph)
DOI: 10.1088/1475-7516/2017/06/048
Cite as: arXiv:1704.07392 [hep-th]

and

Exploring extra dimensions through inflationary tensor modes
Sang Hui Im, Hans Peter Nilles, Andreas Trautner
(Submitted on 12 Jul 2017)
Predictions of inflationary schemes can be influenced by the presence of extra dimensions. This could be of particular relevance for the spectrum of gravitational waves in models where the extra dimensions provide a brane-world solution to the hierarchy problem. Apart from models of large as well as exponentially warped extra dimensions, we analyze the size of tensor modes in the Linear Dilaton scheme recently revived in the discussion of the "clockwork mechanism". The results are model dependent, significantly enhanced tensor modes on one side and a suppression on the other. In some cases we are led to a scheme of "remote inflation", where the expansion is driven by energies at a hidden brane. In all cases where tensor modes are enhanced, the requirement of perturbativity of gravity leads to a stringent upper limit on the allowed Hubble rate during inflation.
Comments: 29 pages, 7 figures
Subjects: High Energy Physics - Phenomenology (hep-ph); Cosmology and Nongalactic Astrophysics (astro-ph.CO); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
Cite as: arXiv:1707.03830 [hep-ph]

and

Strong gravitational lensing --- A probe for extra dimensions and Kalb-Ramond field
Sumanta Chakraborty, Soumitra SenGupta
(Submitted on 18 Nov 2016 (v1), last revised 30 Jul 2017 (this version, v2))
Strong field gravitational lensing in the context of both higher spacetime dimensions and in presence of Kalb-Ramond field have been studied. After developing proper analytical tools to analyze the problem we consider gravitational lensing in three distinct black hole spacetimes --- (a) four dimensional black hole in presence of Kalb-Ramond field, (b) brane world black holes with Kalb-Ramond field and finally (c) black hole solution in f(T) gravity. In all the three situations we have depicted the behavior of three observables: the asymptotic position approached by the relativistic images, the angular separation and magnitude difference between the outermost images with others packed inner ones, both numerically and analytically. Difference between these scenarios have also been discussed along with possible observational signatures.
Comments: Revised version; 29 pages; 11 figures; 4 tables; published in JCAP
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
Journal reference: JCAP 07(2017)045
DOI: 10.1088/1475-7516/2017/07/045
Cite as: arXiv:1611.06936 [gr-qc]

performing these experiments and finding evidence of extra dimensions would validate string/M-theory.

what if,

what if performing these experiments, and others, rule out extra dimensions. obviously there will be peer review, and perhaps more experiments, other explanations might be proposed.

but what if these 2 experiments, and possibly others, rule out Kaluza Klein theories, string theories/M-theory

what-if
these experiments are only consistent in 3 spatial dimensions and 1 time dimension and rule out any additional real dimensions

how would this affect the credibility of string/M-theory?

in light of previous discussion

The problem with those methods of quantization is not just that they are "nonstandard", the problem is that they don't connect with reality in any way! These authors may start classically with known field theories, but when they construct the quantum theory, they do it differently; and the way they do it does not reproduce anything from known physics, not even qualitatively. String theory may usually predict a lot of things we aren't seeing, and a lot of quantities we would like to test remain impossible to calculate; but at least it exhibits qualitative continuity with established physics. All the new phenomena that came with the revival of quantum field theory in the era of the standard model, like anomalies, instantons, you name it, have their counterparts in string theory. On the gravity side, string theory has a classical limit, and it also reproduces theoretical phenomena of semiclassical gravity.

Loop quantum gravity, on the other hand, seems to provide a recipe where you start with a set of fields that includes general relativity, then you follow their special quantization procedure, and you end up with various equations that the resulting wavefunctions have to satisfy, and maybe you can prove one or two things. But these results are entirely abstract and algebraic, and do not give you back anything like quantum fields in space-time, despite the starting point. So this recipe can certainly produce research papers, but the resulting papers are radically disconnected from ordinary quantum field theory, from classical gravity - and from string theory.

Once I concluded that the divide is really that great, I became perplexed by the size and persistence of the loop quantum gravity literature. I can see one person, or a handful of people, stubbornly persevering in a research program that disdains lots of established physics, due to an idiosyncratic investment in particular ideas. But loop quantum gravity is dozens of people over decades. I was especially troubled by the lack of historical precedent for this.

But I'm happier now because I did find a historical analogy: algebraic quantum field theory. It's not an exact analogy, but it is another example of a research community developing over decades a mathematical formalism which is largely disconnected from what physicists were actually doing. Algebraic quantum field theory starts with a few ideas drawn from real physics, but describes either fields that don't interact, or a few special interacting field theories in lower dimensions. Meanwhile, real physicists were using effective field theory, the renormalization group, and the lattice. Similarly, loop quantum gravity started with some real things, but its subsequent development has diverged from everything in gauge theory and quantum gravity that actually works.

Returning to the idea that some sort of standard but nonperturbative canonical quantization of supergravity might help with the formulation of M-theory, well, it might help just because it would be in that same mainstream of quantization methods, and would therefore actually be relevant to M-theory. But I think that at best it would still only give you a new perspective on what's missing in supergravity. In the end you should find that you need new heavy states, the branes. The best guide might be AdS/CFT in the case of AdS4/CFT3 and AdS7/CFT6, where known CFTs are believed to be entirely equivalent to M-theory in the dual AdS spaces.

and

There is a whole list of reasons why this is overly naive.

First, the idea that a choice of coordinates on phase space (e.g. Ashtekar variables) should affect the outcome of quantization is in contradiction with basic facts of physics. On the contrary, everything ought to be independent of artificial choices of parameterizing phase space, even if maybe one choice of coordinates may make some aspects more transparent than others. But if you find yourself with a would-be quantization that only works in one set of "variables" but not in another, then something went wrong.

Second, gravity is not fundamentally a gauge theory as Yang-Mills theory is, even if you write it in first-order language in terms of a vielbein and a spin connection. The spin connection is an auxiliary field that serves to implement the torsion freeness constraint, but the genuine field of gravity is encoded in the vielbein. Mathematically the statement is that a field configuration of gravity is equivalently encoded in a variant of an affine connection, yes, but the full structure is that of a Cartan connection This is a plain affine connection plus extra data and constraints. Glossing over this point is the source of much confusion in the literature.
...

what becomes of string M-theory and Urs Schreiber and mitchell porter observations and objections if on experimental grounds, using experiments and observation, extra dimensions are completely ruled out, and that experiments are only consistent with 3+1 dimensions?

what would be the most promising approach to quantum gravity 3+1 dimensions should experiment and observation rule out Kaluza Klein dimensions if it's not loop quantum gravity?

bonus - what would be the most promising approach to quantum gravity 3+1 dimensions should experiment and observation rule out Kaluza Klein dimensions and supersymmetry if it's not loop quantum gravity?

 

[Urs Schreiber]

what would be the most promising approach to quantum gravity

Notice that the technical term "non-renormalizable" that goes with "gravity" is dangerously misleading: It does not mean that the usual perturbation theory for QFT fails for gravity, it just means that the "counter term"-parameters that need to be picked/measured at each loop order don't break off at some loop order, but keep coming. There is nothing logically problematic with choosing (or incrementally measuring as one keeps increasing accelerator energy) an infinite stream of parameters. Hence perturbative quantum gravity is mathematically well defined, has been constructed, and does make predictions (iteratively in energy scales). Do check out the references on this here.

The next step is to explore plausible algorithms that produce choices of infinite lists of counter-terms from less input data. Two classes of examples of such are known:

One is "asymptotic freedom", the other is perturbative string theory.

In the former case one tries to identify finite-dimensional subspaces in the infinite-dimensional space of choices that are characterized by a certain property of the RG flow. If these indeed do exist (which is open) then saying "let the infinite array of coupling constants sit on one of these" is a way of encoding an infinite number of choices in a few words, and leaving just a finite number of choices. The result however is still a perturbative QFT.

In perturbative string theory instead the list of counterterms is re-encoded into a choice of 2d SCFT (a "perturbative string vavuum"). While hopes have decreased that this re-encoding actually shrinks the space of choices considerably, the bonus is that the previously random list of counter-terms now gets a "meaning" and, more importantly, a dynamics which allows to see hints of what might actually be going on beyond perturbation theory. Of course even so, none of this may be realized in nature. This is your worry.

To truly go beyond the perturbative theory, new ideas and results are necessary. Notice that this is not a problem with just gravity either. We have NO non-perturbative quantization of ANY interacting quantum field theory in dimensions four or higher (apart from numerical simulation).

 

[mitchell porter]

what if performing these experiments, and others, rule out extra dimensions

Not one of those experiments can rule out extra dimensions. At best they can rule out "large" extra dimensions, which have always been a special type of model, not the most straightforward.

Also, it is not technically the case that string theory demands more than 3 dimensions of space. For the actual physics to be unaffected by the coordinate system we employ inside the string (along its length in space, along its worldline in time), its "conformal anomaly" needs to cancel. One way for this to happen is to work in the critical dimension of 9 space, 1 time. But another way is to have internal fermions that are attached to the string and move along it. With enough of these, you can work directly in 3+1 dimensions.

So I don't count on any special evidence for string theory like large extra dimensions, exotic charged particles, or peculiar CMB effects. It's fine for people to notice such possibilities. But I consider the real task of string phenomenology to be, reproducing what we already see, and explaining what the standard model doesn't explain, like those two dozen unexplained SM parameters.

That is considered very hard, both because of the vast number of string vacua to consider, and because of the difficulty of calculating the low-energy physics. But people are making progress, and they are even starting to use AI techniques to quickly search through lots of vacua for desired properties.

If the correct vacuum was found, it should be very predictive, because it would determine all the SM constants, in as much detail as you want to calculate or measure. The hard thing is finding it, and knowing that you have found it.

 

[kodama]

what about theories like gravity as quantum entanglement

Not one of those experiments can rule out extra dimensions. At best they can rule out "large" extra dimensions, which have always been a special type of model, not the most straightforward.
.

what kind of experiment could test, or rule out, "small" extra dimensions, in principle?

 

[PAllen]

Not one of those experiments can rule out extra dimensions. At best they can rule out "large" extra dimensions, which have always been a special type of model, not the most straightforward.

Also, it is not technically the case that string theory demands more than 3 dimensions of space. For the actual physics to be unaffected by the coordinate system we employ inside the string (along its length in space, along its worldline in time), its "conformal anomaly" needs to cancel. One way for this to happen is to work in the critical dimension of 9 space, 1 time. But another way is to have internal fermions that are attached to the string and move along it. With enough of these, you can work directly in 3+1 dimensions.

So I don't count on any special evidence for string theory like large extra dimensions, exotic charged particles, or peculiar CMB effects. It's fine for people to notice such possibilities. But I consider the real task of string phenomenology to be, reproducing what we already see, and explaining what the standard model doesn't explain, like those two dozen unexplained SM parameters.

That is considered very hard, both because of the vast number of string vacua to consider, and because of the difficulty of calculating the low-energy physics. But people are making progress, and they are even starting to use AI techniques to quickly search through lots of vacua for desired properties.

If the correct vacuum was found, it should be very predictive, because it would determine all the SM constants, in as much detail as you want to calculate or measure. The hard thing is finding it, and knowing that you have found it.

The first paper linked in the OP explicitly discusses s non compact and l compact dimensions of order plank length, and proposes possibly measurable effects of the l compact dimensions.

 

[mitchell porter]

The first paper linked in the OP explicitly discusses s non compact and l compact dimensions of order plank length, and proposes possibly measurable effects of the l compact dimensions.

They talk about the thermodynamics of a condensate of rubidium atoms. Rubidium atoms have an internal structure. To condense, they have to be delocalized on a scale larger than that structure. All the physics relevant to their thermodynamics has to occur on those scales. So if the compact dimensions are that small, they are thermodynamically irrelevant and the effective value of l in their formulas has to be zero.

what kind of experiment could test, or rule out, "small" extra dimensions, in principle?

Let's think about what extra dimensions entail. Throughout macroscopic space, what appears to be a point is actually a compact space. It has a shape and a size. If the shape is complicated, there may be many size parameters, called moduli (plural of modulus). In principle, these parameters can vary since geometry is dynamic, but in practice they must be stabilized very tightly around specific values, since the SM parameters are in turn functions of the moduli. For example, if a gauge force comes from strings attached to a particular brane, the coupling constant will depend on how much of the extra-dimensional volume is occupied by the brane. Or, if yukawa couplings involve a three-way interaction between a Higgs string and two chiral fermionic string-states, the coupling will depend on the triangular surface area of that open string interaction.

The sort of "test of extra dimensions" that I would hope for is, as I said earlier, a direct explanation of SM structure and parameter values in terms of a specific compact geometry. However, because such a theory has all that extra plumbing, there must be BSM states and processes too. Basically, you might have Kaluza-Klein excitations of a particle's wavefunction, or you might have excitations of the geometry itself. You would expect both of these to require enormous energies akin to the grand unification scale. So if you had a particle collider of astronomical size, it can directly produce these new states. Or, there might be a process like proton decay, very rare because it is a quantum tunneling event which requires a KK-scale energy fluctuation, but which would occur occasionally in bulk.

In string theory, moduli refers not only to the size parameters of the compact geometry, but also to "particles" which are actually excitations of that geometry. There might be a closed loop in the compact geometry, and there could be an excitation along that loop. A common theme in string cosmology is moduli particles, produced in the early universe, which persist as dark matter... You would expect that moduli particles can only be produced by very high energies, just on the grounds that if they could be produced more easily, they would mess up low-energy physics. But in fact the masses of moduli are highly model-dependent. They can be very light.

So the situation here might be like it is in field theory. There could always be a new type of particle to be found at the next energy scale, and perhaps moduli are candidates for that. I don't have much grasp of the details here, the theoretical constraints, I haven't studied this area at all. I just mention it because the coupling constants and the yukawas should be functions of the moduli, and so there might be some deviation from SM behavior, if moduli excitations get involved. But this would be highly model-dependent, and without already having a specific string vacuum in mind, you wouldn't know that such an effect involved extra dimensions, it would just be "new particle".

I would therefore sum it up like this. Observing small extra dimensions should in general require enormous energies. It could happen at lower energies if there happen to be light moduli - either dark matter moduli, or moduli that determine SM parameters. But I think the best bet for validating extra dimensions, is for someone to find a string vacuum that actually produces the SM.

what about theories like gravity as quantum entanglement

What about them? :-)

 

[PAllen]

They talk about the thermodynamics of a condensate of rubidium atoms. Rubidium atoms have an internal structure. To condense, they have to be delocalized on a scale larger than that structure. All the physics relevant to their thermodynamics has to occur on those scales. So if the compact dimensions are that small, they are thermodynamically irrelevant and the effective value of l in their formulas has to be zero.

That's not what they say. l is a number of compact dimensions of Planck scale or smaller. I notice no redefinition of l in their paper. It may well be the paper is wrong, I cannot judge its details, but what you say does not correspond to what I read in the paper.

 

[mitchell porter]

That's not what they say.

Right, I'm pointing out something that the paper overlooks.

 

[Urs Schreiber]

Also, it is not technically the case that string theory demands more than 3 dimensions of space. For the actual physics to be unaffected by the coordinate system we employ inside the string (along its length in space, along its worldline in time), its "conformal anomaly" needs to cancel. One way for this to happen is to work in the critical dimension of 9 space, 1 time. But another way is to have internal fermions that are attached to the string and move along it. With enough of these, you can work directly in 3+1 dimensions.

Or a non-constant dilaton, or yet other effects.

Just to amplify this point:

What critical perturbative string theory really demands is that it is based on a 2d SCFT of central charge 15. (That number comes from quantizing the generally diffeomorphism invariant super-Polykov action, by gauge fixing the diffeomorphism invariance to leave only conformal invariance and adding the corresponding diffeomorphism Fadeev-Popov ghosts. The diffeomorphism ghost systems turns out to have central charge -15, and hence to cancel that the remainder must be an SCFT of central charge 15).

For sigma-model 2d SCFTs, i.e. those that come from a geometric background manifold spacetime and for constant dilaton, each dimension of the target manfold contributes 1.5 to the central charge (one for the corresponding worldsheet boson and one half for the corresponding worldsheet fermion). This is how one arrives at a critical dimension of 10.

But there are 2d SCFTs that are not sigma-models, but are purely algebraically defined. Most famous are the Gepner models. These describe degenerations where a target spacetime becomes degenerate. There is no reason to believe that geometric sigma-models are preferred among all 2d SCFTs. The full moduli space of 2 SCFTs of central charge 15 (the true pertrubative "landscape") is widely unknown.

So if the extra 6 dimensions -- really the extra 6 x 1.5 = 9 central charge -- is given by a non-geometric model, there is no particular reason that this would be seen in experiment as actual extra dimensions.

If we pass from 2d SCFTs to their point particle limit, known as "spectral triples", then this effect is maybe better known. There is a spectral triple of KO-dimension 10 and classical dimension 4, with a "compact" algebraic piece of KO-dimension 6 and classical dimension 0, which comes very close to the standard model in 4d. This is discussed in the PF-Insights article Spectral Standard Model and String Compactifications.

Of course for genuine perturbative string theory, hence for 2d SCFTs instead of just spectral triples, the situation is more subtle. All the more does the conclusion hold that it is not automatic that critical perturbative string theory implies that there are internal dimensions that are detectable as spatial dimensions in the usual way.

 

[kodama]

Not one of those experiments can rule out extra dimensions. At best they can rule out "large" extra dimensions, which have always been a special type of model, not the most straightforward.

Also, it is not technically the case that string theory demands more than 3 dimensions of space. For the actual physics to be unaffected by the coordinate system we employ inside the string (along its length in space, along its worldline in time), its "conformal anomaly" needs to cancel. One way for this to happen is to work in the critical dimension of 9 space, 1 time. But another way is to have internal fermions that are attached to the string and move along it. With enough of these, you can work directly in 3+1 dimensions.

If the correct vacuum was found, it should be very predictive, because it would determine all the SM constants, in as much detail as you want to calculate or measure. The hard thing is finding it, and knowing that you have found it.

are there any falsifiable predictions that come from "internal fermions that are attached to the string and move along it"

 

[mitchell porter]

are there any falsifiable predictions that come from "internal fermions that are attached to the string and move along it"

There is a whole subfield of string phenomenology based on this, the "free fermionic models". It seems to be at a level similar to other forms of string phenomenology - the best models give you (e.g.) mass matrices which resemble the standard model, but calculating exact values is still too hard, and non-supersymmetric vacua have still hardly been studied.