The Holey Grail and its Dual: From String Theory to Strange Metals

Quantum Gravity: The Holey Grail.

Jonathan Granot’s colloquium slides have an amusing typo rendering quantum gravity the “holey grail of physicists.” How appropriate, I thought, and many of these holes are black. But typo aside, how holy really is this grail to physicists? After all, other areas of physics have their own holey grails: quantum computing for example, or high temperature superconductivity.

High temperature superconductors are badly understood theoretically, yet this understanding might allow us one day to create superconducting materials that save energy by avoiding resistive losses in long distance power lines. Imagine the potential! (Alternatively, read this.)

Presently the temperature at which these materials become superconducting is “high” only to the physicist who spends his days playing with liquid nitrogen: The transition temperature below which superconductivity sets in, also called the critical temperature, is in all known cases below -70°C. (The value depends on properties of the material as well as external fields.)

“Normal” superconductivity is described by the theory of Bardeen, Cooper and Schrieffer. At low temperatures, but in the not-superconducting phases, these metals are well described as Fermi liquids. But metals who display high temperature superconductivity are an entirely different story, and one that is largely unwritten.

One thing we know from experiment is that high temperature superconductors are “strange metals” whose electric resistance in the normal, non-superconducting, phase increases linearly with the temperature rather than with the square of the temperature. The latter is what one finds for a Fermi liquid with weakly coupled quasi-particles. Thus, plausibly the reason for our lacking theoretical understanding is that strange metals are strongly coupled system, which are notoriously hard to understand. “But darling,” said the string theorist, “I can explain everything.” And so he puts a black hole into an Anti-DeSitter (AdS) space and looks at the boundary.

The celebrated AdS/CFT correspondence makes it possible to deal with strongly coupled systems by mapping them to a weakly coupled gravitational system in a space-time with one more dimension. This is computationally more manageable, or at least one hopes so. So far, this correspondence, also called “duality”, between the gravity in the AdS space and the strongly coupled theory on the boundary of this space (thus one dimension less) is an unproved conjecture put forward by Juan Maldacena. However, it has been extensively tested for a few cases and many people are confident that it captures a deep truth about nature (though they might disagree on the extent to which it holds). We previously discussed this idea here and here.

For a high-temperature superconductor, one puts a planar black hole in the AdS space and decorates it with some U(1) vector fields and a scalar field, φ, and then goes on to calculate the free energy for different configurations of the scalar field. For temperatures above a critical value, the free energy is minimal if the scalar field vanishes identically. However, if the temperature drops below this critical value, configurations with a non-vanishing scalar field minimize the free energy, so the system must make a transition. In the figure below, you see the free energy, F, (with some normalization) as a function of the temperature (again with some normalization) for the case of φ = 0 (dotted line) and a case with non-vanishing φ (solid line). The latter solution doesn’t exist for all values of the temperature. But note that when it exists, its free energy is lower than that of the φ=0 solution.

[Image credits: Hartnoll, Herzog and Horowitz]

For these different configurations one can then calculate thermodynamic quantities of interest, such as the electric conductivity (AC and DC) or heat conductivity, and… compare the results with actual measurements.

As you can tell already from my brief summary, this approach to understand strange metals is, presently, far too rough to give quantitative predictions. It can however describe qualitative behavior, such as the scaling of the resistance with temperature that is so puzzling. And that it does quite well!

A bunch of smart people have been studying the strange metal duals for a couple of years now, among others Subir Sachdev, Sean Hartnoll, Hong Liu (who wrote a recent article for Physics Today on the topic), Shamit Kachru, Gary Horowitz, and a group here at Nordita around Lárus Thorlacius.

An exciting recent development is that Horowitz et al added a lattice structure by a periodic boundary condition, which is a big step towards modeling more realistic systems. Amazingly, despite the simplicity of the model, they scaling they find for the optical conductivity (the ability of photons to pass through a material) as a function of the photon’s frequency is in excellent agreement with experiment. (See “Optical Conductivity with Holographic Lattices” Gary T. Horowitz, Jorge E. Santos and David Tong, arXiv:1204.0519 [hep-th]).

One of the side-effects of commuting from Heidelberg to Stockholm is that the door sign with my name spontaneously relocates when I’m not at the institute, and I acquire new office mates in this process. Which is how I came to talk to Blaise Goutéraux, who arrived at Nordita this fall.

Blaise is among the AdS/CFT correspondents of Nordita’s “subatomic” group. (In fact, at this point I seem to be the only one in this group who doesn’t have anything to do with bulks and branes.) Blaise has taken on another challenge in this area, which is to describe the landscape of holographic quantum critical points, from which the strange metallic behavior at finite temperature is believed to originate. For this, he is working with more complicated geometries that exhibit different scaling behaviors from AdS.

What do we learn from this? The AdS/CFT correspondence is a useful tool, and if you’ve got a hammer quantum critical points might start looking like nails. But the only reason we call the bulk theory gravitational is that we first encountered a theory of this type when we wanted to describe the gravitational interaction. Leaving aside this scientific history, in the end it’s just a mathematical model to calculate observables that can be compared to experiment. And that’s all fine with me.

The big question is however whether this approach will ever be able to deliver quantitative predictions. For this, a connection would have to be made to the microscopic description of the material, a connection to the theories we already know. While this is not presently possible, one can hope that one day it will be. Then one could no longer think of the duality as merely useful computational tool with an educated guess for the geometry – the bulk theory would have to be a truly equivalent description for whatever is going on with the lattice of atoms on the boundary. But the cases for which the AdS/CFT correspondence has been well tested are very different from the ones that are being used here, and the connection to string theory, the original inspiration for the duality, has almost vanished. It wouldn’t be the first time though that physicists’ intuitions are ahead of formal proof.

Is a tabletop search for Planck scale signals feasible?

In a recent arxiv paper, Jacob Bekenstein from the Hebrew University of Jerusalem proposed a tabletop experiment to test Planck scale signals:

Is a tabletop search for Planck scale signals feasible?
Jacob D. Bekenstein
arXiv:1211.3816 [gr-qc]

The idea is roughly the following: Take a single photon and spread its wavefunction by suitable lenses, then let it hit some macroscopic solid block, for example a crystal. Focus the photon and detect it.

Since the crystal has a refractive index, the photon has to discard momentum into it. This momentum will be evenly spread into the crystal, distributed by phonons, and be returned to the photon upon exit. Essentially, the block reacts not like single atoms but in one piece (though it cannot instantly do so, the distribution of momentum must take a finite amount of time).

If you give the crystal a momentum for the duration of the photon’s passage, it will move, but since it’s macroscopically heavy, it will move only a tiny distance. If you look at the shift of its center-of-mass, the distance it will move scales with the energy of the incoming photon over the mass of the block.

Bekenstein puts in the numbers and finds that with presently available technology, the energy of a single photon could be so tiny that the distance the crystal moves would have to be smaller than the Planck length. This, he argues would “occasionally be at odds with the non-smooth texture of spacetime on Planck scale.” If that is so, the photon would not be able to transverse the crystal, leading to an unexpected, and observable, decrease in the transmission probability.

He also estimates sources of noise that could move the block oh-so slightly and affect the probability of the photon trespassing, thus rendering the outcome inconclusive. Bekenstein argues that by cooling the block to some Kelvin, which is cold indeed but still feasible, the noise could be kept under control. This might seem implausible at first sight, but note that the thermal noise for the motion of the center-of-mass itself is not the problem because the photon spends only a very short time inside the crystal. The relevant question is whether the center-of-mass moves in that short duration. 

So far, so brilliant. The proposed experiment is an excellent example for a model-independent test. It is so model-independent in fact that I don’t know which model could be constrained by it.

The usual expectation from Planck-scale fluctuations is that they lead to a position uncertainty that cannot become smaller than the Planck length. This does not forbid you to move an item by distances less than the Planck length, it just tells you that the position of the crystal wasn’t defined to a precision better than the Planck length to begin with.

Now, if space-time was a discrete regular lattice with Planck-length spacing then you could not move the crystal, as a rigid block, by anything shorter than the Planck length. Already if the lattice isn’t regular, this is no longer true. But even if the lattice was regular, the crystal would have to be very rigid indeed, so as to not allow any relative shift among atoms that could account for the motion of the center-of-mass. For example, if your block has a number of particles about Avogadro’s number, 10²³, and you move one out of 10¹⁵ of these atoms by a distance of 10^-20 m (that’s less than the size of a proton and less than the LHC can probe), you’d move the center of mass by about a Planck length. Now I don’t know much about crystals, but it seems quite implausible to me that the effective description of phonons on the lattice should be sensitive to such tiny shifts at all (even worse if the block is not a crystal but some amorphous solid).

Besides this, I don’t understand how the “rejection” of the photon should come about if one took the path integral of all possible trajectories and scatterings in the crystal, none of which is sensitive to Planck scale effects.

In summary: The proposed table-top argument tests a quantity, the shift of the crystal’s center-of-mass, which is of the order Planck length. It is unclear however if there is any plausible model for the phenomenology of quantum gravity that would be constrained by this a measurement. Is a tabletop search for Planck scale signals feasible? Maybe. Is it possible with the proposed experiment? Probably not. Does it have to do anything with Planck mass black holes? No.

There's no free lunch - and no free news either

I read last week that the German daily newspaper "Frankfurter Rundschau" declared bankruptcy. While it's not the first and probably not the last newspaper to throw in the towel, this saddened me considerably because it's the newspaper I've grown up with. Some years ago, when back in Europe, I checked their website and found it confusing to useless. I never gave it a second look, and haven't bought a print issue since forever. So to make matters worse now I feel personally responsible for sinking a newspaper I actually thought was pretty good. I also haven't bothered you for a while with my terribly insightful diagrams, so here are two to depict the problem.

The first one shows the present situation of online news providers. We get the news "for free" because they're paid by advertisement revenue. But this money has to come from somewhere, so we pay for it with the product that's being advertised. Now nobody really likes all the advert clutter around or even covering the news, and advertisement techniques are shifting. The problem is then that if newspaper advertisement doesn't yield results, and companies cut it out of the cycle, they cut off your news feed with it. What bothers me even more is that long before this happens newspapers have a large incentive to produce content that increases the number of people clicking on adverts. It is questionable this benefits the quality of information.

The second diagram shows how the situation would look like if we'd manage to get over the idea that information is free. All content has to be produced somewhere by somebody and that somebody needs to live from something. It would make more sense to directly pay for news because the feedback loop isn't distorted by product sales. If you cut out the marketing here, you cut yourself off information about products and services, which would lead to incentives for more sensible advertisement rather than to incentives for more traffic-generating content aggregation.

Most providers of online news actually represent a mixture of these two cases, but the first case has become very dominant within the last decade or so. During the last years there has been a trend to subscriptions for online content, notably realized by the NYT paywall. Now the NYT is a very prominent newspaper with a large readership, and that it seems to be working for them doesn't mean it will be working for everybody. The problem is that the subscribers still pay, implicitly, for the advertisement cost with purchase of products. As long as there are news financed entirely or to a large extent by adverts, capitalism predicts people will prefer them (unless they are of considerably worse quality that is), and it will be very difficult for pay-for-content news providers to generate enough revenue.

Book review: “Brain Bugs” by Dean Buonomano

Brain Bugs: How the Brain's Flaws Shape Our Lives
By Dean Buonomano
W. W. Norton & Company (August 6, 2012)


We have to thank natural selection for putting a remarkably well-working and energy-efficient computing unit between our ears. Our brains have allowed us to not only understand the world around us, but also shape nature to suit our needs. However, the changes humans have brought upon the face of the Earth, and in orbit around it, have taken place on timescales much shorter than those on which natural selection works efficiently. And with this comes the biggest problem mankind is facing today: We are changing our environment faster than we can adapt to it - evolution is lagging behind.

The human body did not evolve to sit in an office chair all day long, neither did we have time to adapt to an overabundance of food, travel over different time-zones, or writing a text-message while driving on a 6-lane highway. We have absolutely no experience in governing the lives of billions of people and their impact on ecological systems. These are not situations our brains are well suited to comprehend.

There are four ways to deal with this issue. First, ignore it and wait for evolution to catch up. Not a very enlightened approach as we might go extinct in its execution. Second, the Amish approach: keep the environment in a state that our brains evolved to deal with. Understandable, but not for the curious and not realistically what most people will sign up to. Third, tweak our brains and speed up evolution. Unfortunately, our scientific knowledge isn't yet sufficient for this, at least not without causing even larger problems. This then leaves Fourth: Learn about our shortcomings and try to avoid mistakes by recognizing and preventing situations in which we are prone to make errors of judgement.

I recently reviewed David Kahneman's book "Thinking, Fast and Slow", which focuses on a particular type of shortcoming in our judgement, that is that we're pretty bad in intuitively estimating risks and making statistic assessments. Dean Buonomano's book includes these biases that are focus of Kahneman's work, but offers a somewhat broader picture, covering other "brain bugs" that human have, such as memory lapses, superstition, phobias, and imitative learning. Buonomano is very clear in pointing out that all these "bugs" are actually "features" of our brains and beneficial in many if not most situations. But sometimes what is a useful feature, such as learning from others' mishaps, can go astray, as when watching the movie “Jaws” leaves people more afraid of being eaten by sharks than of falling victim to heart attacks.

Dean Buonomano is professor for neurobiology and psychology at UCLA. His book is easy to follow and well written. It moves forward swiftly, which I have appreciated very much because it turns out I knew almost everything that he wrote about already, a clear sign that I have too many subscriptions in my reader. The illustrations are sparse but useful, the endnotes are helpful, and the reference list is extensive.

I have only one issue to take with this book, which is that Buonomano leaves the reader with little indication on how well established the research is that he writes about. In some cases he offers neurological explanations for "brain bugs" that I suspect are actually quite controversial among specialists - it would be surprising if it wasn't so. He has an interesting opinion to offer on the origin of religious beliefs that he clearly marks as his own, but in other instances he is not as careful. Since I'm not an expert on the topic, but generally suspicious about results from fields with noisy data, small samples, and large media attention, I'm none the wiser for what the durability of the conclusions is concerned.

In summary: This book gives you a good overview on biases and shortcomings of the human brain in a well-written and entertaining way. You will not get a lot of details about the underlying scientific research, but this is partly made up for with a good reference list. I'd say this book deserves four out of five stars.

Thin Nematic Films: Liquid Beauty

Image source: arXiv:1010.0832 [cond-mat.soft]

No, it's not a moon passage in front of an exoplanet. It's a thin nematic film. Let me explain.

Between condensed matter physics and chemistry, between solids and liquids, there is soft condensed matter. Soft condensed matter deals with the behavior of materials like gels, glasses, surfactants, or colloids. Typically these are fairly large molecules, possibly floating in some substrate, and can assemble to even larger structures. Understanding this assembly, the existence of different phases, and also the motion of the molecules is mathematically challenging due to the complexity of the system.

But taking on this challenge is rewarding: Soft matter is all around you, from toothpaste over body lotion to salad dressing. It is even quite literally in your veins. One of the best known examples for soft matter however is probably not blood, but liquid crystals.

Liquid crystals are rod-like molecules whose chemical structure encourages them to collectively align. How well this works depends on variables in the environment, for example temperature and magnetic fields. Liquid crystal have different phases; the transition between them depends on these environmental variables. In the so-called nematic phase molecules are locally aligned but still free to move around, and the orientation might change over long distances.

To make the molecule orientations visible, one uses polarized light on a thin film of liquid crystals on some type of substrate and a polarization filter to take the image. The liquid crystal molecules change the polarization of the light depending on the molecules' orientation, so different light intensities become a measure for the orientation of the molecules.

For the images we are looking at here we have the substrate below the liquid crystal and air above it. These two different surfaces causes a conundrum for the molecules in the liquid crystal, because they would prefer to align parallel to the substrate, but vertical to the air surface. Now if the film is fairly thick - "thick" meaning a μm or more - the molecules manage to align along threads that bend to achieve this orientation, though there are the occasional topological defects in this arrangement, places where the molecules change orientation abruptly. This is what you see for example in the image blow

[Picture Credits: Oleg Lavrentovich from the Liquid Crystal Institute at Kent State University, for more pictures see here.]

But this behavior changes if the film becomes very thin, down to a tenth of a μm or so. Then, the competing boundary conditions from the two interfaces start getting in conflict with the molecules' desire to align, which breaks the symmetry in the plane of the liquid and leads to the formation of periodic structures, like the ones you see in the first image. In this example, the nematic film does not cover the whole area shown, but it's a drop that covers only the parts where you see the periodic structures. This has the merit that one can see that the orientation of the structure to the boundary is always perpendicular.

The typical molecules in these films are not very large. In the example here, it's 6CB with the chemical structure C₁₉H₂₁N. The size of this molecule is much smaller than the width of the film when the effect sets in, so this cannot be the relevant scale. The question at which width the instability sets in has been studied in this paper, where also the image was taken from. It's an intriguing effect that can teach us a lot about the behavior of these molecules, not to mention that it's pretty.

CMB anisotropy, 13 years later

Sean wrote a wonderful post about the recent measurement of the anisotropies in the cosmic microwave background from the South Pole Telescope. I am so impressed by the data. To give you a visual impression on just how dramatically the measurements have improved, I've dug out an old plot from 1999. (Note the square root in the vertical axis though.)

Fig1: CMB power spectrum, 1999, data from Python (star) and Viper (box). Image source.

Fig 2: CMB power spectrum, 2012, data from WMAP7 and SPT.  Image source.

For more information about the CMB anisotropies, please refer to this or this earlier post.

Program: Run your own!

This month, we have a program on "Perspectives of Fundamental Cosmology" here at Nordita, which I've been organizing together with Martin Bojowald, Kristina Giesel and Mairi Sakellariadou. Since it's a format for scientific meetings that is not so common, I thought it would be worthwhile to tell you a few words about it.

The purpose of running a program is to get researchers together for an extended amount of time, to give them the opportunity not only to get to know each other and share their ideas, but also have the time and space to work on this ideas, discuss them, and to find new collaborators. A workshop or a conference is usually too short and the schedule too packed to really allow participants to have much constructive exchange. And in contrast to a school, the talks and lectures at the program are usually focused on a specific topic and its challenges. The programs are really meant to move a field forward, and to allow people to work on this actively. Though, if you have a student who is beginning his own research agenda, sending him or her to a program on the topic will make for a good start.

The programs at Nordita are very similar to the programs at the KITP in Santa Barbara, and in some cases a longer program goes together with a shorter workshop or conference on the same or a closely related topic.

Does the idea of getting together with likeminded researchers for 4 weeks in Stockholm to dig into a problem sound good to you? You can submit a proposal for your own program here; this year's deadline is November 15. The topic should be in theoretical physics or a closely related area of the natural science. If your proposal is selected, you'll get a grant to invite people and can basically arrange the schedule as you please. And let me not forget to mention that while Santa Barbara has the nicer beaches, Stockholm is arguably a more interesting place than Goleta.

If you want to know more about Nordita, check out our information brochure (pdf, 4.5 MB).

Interna

Gloria trying out my
running shoes.

Fall has come to Germany and with it a bunch of bad news. The grant application that I had written in spring didn't go through, and the Swedes want EUR 1,500 additional taxes for the calendar year 2011. My last grandparent died, so now another generation of my family is on the cemetery "watching radish from below" as the Germans say so aptly. Also our landlord died, unexpectedly, last month. Now his wife owns the building but she isn't up to dealing with the details and handed over responsibility to an apartment management company. We're awaiting the changes this might bring, and I for once am glad I insisted on writing down every little detail into the lease, thinking to myself: what if he dies and his wife can't recall what we agreed upon.

We're also fighting again with the German "Familenkasse" for our child benefits. They had informed us at the beginning of the year (after a full year of struggle with them) that Stefan would finally get the usual monthly rate, and that retroactive back to the girls' birth. Alas, after a few months they stopped paying and he never saw a cent for the first year. They didn't give any reason for this.

After we waited for some while to see if any information would trickle down our direction, I finally lost patience and spent an hour or so trying to get somebody on the phone. Amazingly enough, they have no waiting loop, but just disconnect you if all lines are busy. Yes, that's right, I actually had to call their number over and over again. And then all I got was a call-center where they evidently had no information in Stefan's files about what was going on. So much about German efficiency.

Upon my question if they could maybe connect me to the local office that was actually responsible for this nonsense they said, no they can't connect me and there's no way to reach them by phone, I can only appear there in person if I really want. Or my husband, respectively, as it's actually his application.

As much as I like my iPhone, it's a serious disadvantage that you can't slam down the receiver.

By coincidence I then came across a website of the European Union where they offer a service called SOLVIT whose sole purpose seems to be to help with this type of communication problem between national institutions of the European Union. So now I submitted our case. I heard from them within 24 hours and they promised they'll take on the problem. I'm curious if they'll manage to sort this out, stay tuned.

The kids meanwhile are having fun taking apart the furniture and pushing all buttons that they can get their hands on. Everything that beeps is particularly interesting, for example the microwave and the babyphone. To help align Lara's gaze she now has to wear an eye patch a few hours a day. We were expecting protest, but she doesn't seem to mind. The biggest problem is that it hurts when torn off. Needless to say, Gloria will cry and scream until she also gets an eye patch, which we put on her cheek. Stefan and I also sometimes wear one. Lara probably meanwhile thinks it's a strange kind of fashion.

Our November program on "Perspectives of Fundamental Cosmology" is starting on Monday, and the next weeks will be very busy for us. After that I hope things slow down towards the end of the year.

Lara with her eye patch.