Not Even Wrong

It’s becoming clear what the hot new topic in particle theory is these days: the use of twistor space methods to try and understand scattering amplitudes in Yang-Mills and gravity theories, especially the maximally supersymmetric versions. This evening on the arXiv there are two closely related papers on the topic: Scattering Amplitudes and BCFW Recursion in Twistor Space by Lionel Mason and David Skinner, and The S-Matrix in Twistor Space, by Arkani-Hamed and collaborators (there’s also a third, much more distantly related paper, this one). The Arkani-Hamed et al. paper gives an extensive discussion of motivation for this work in the introduction: the structure of scattering amplitudes for these theories is remarkably simple in twistor space, leading to the question of whether one can formulate the full theory directly in twistor space somehow, giving a different sort of holographic dual than the AdS/CFT one.

A very influential version of this idea goes back to Witten’s 2003 paper Perturbative Gauge Theory as a String Theory in Twistor Space, where the dual theory investigated was a topological string theory. This most recent work doesn’t appear to use topological string theory, although Arkani-Hamed et al. are rather cagey on the topic of what sort of twistor space theory is at issue. They promise a forthcoming paper entitled “Holography and the S-matrix”, with:

a completely different picture for computing scattering amplitudes at tree level than given by the BCFW formalism, that we strongly suspect is connected with a maximally holographic description of tree amplitudes that makes all the symmetries of the theory manifest but completely obscures space-time locality.

The history of using twistor-space to study gauge theory goes back a very long ways. Penrose started using twistor techniques to study gravity back in the mid-sixties, and after the 1975 discovery of self-dual solutions to the YM equations (instantons), it became apparent that twistor-space techniques could be used to solve them, turning the problem of solving these non-linear equations into a problem in algebraic geometry, that of constructing certain holomorphic vector bundles. Atiyah was among the mathematicians who got interested in this, and his beautiful 1979 lecture notes Geometry of Yang-Mills Fields remain a wonderful introduction to the mathematical side of the subject. While still a post-doc, Witten worked in this area, coming up in 1978 with an interpretation of the full YM equations using supersymmetry. Work on this topic was what brought Atiyah and other mathematicians into contact with physicists, including Witten, beginning a quite remarkable period of very successful interaction between the two camps.

Twistors were among the things I started thinking about at the end of my graduate school days in the mid-eighties, for a completely different reason, one that has nothing to do with the current interest in the subject. I was interested in the problem of how to put spinors on a lattice, and the twistor geometry story gives a beautiful way of thinking geometrically about spinors. This idea never really got anywhere, although I did notice some relations between the geometry of the standard model gauge groups and representations that I wrote about back in 1987 and still find quite remarkable. It will be interesting to see what new ideas emerge from this latest wave of interest in thinking about quantum field theory in twistor-space.

LHC media fever continues this year, with at least three books out or on the way:

The Quantum Frontier: The Large Hadron Collider by Fermilab experimentalist Don Lincoln.

Collider: The Search for the Worlds Smallest Particles by Paul Halpern.

and

The Large Hadron Collider by Lyn Evans, who knows a thing or two about the subject.

There’s also a documentary entitled Particle Fever being made about the LHC, produced by theorist David Kaplan, who “has discovered some of the most recognizable extensions to the standard model of elementary particles.” The film web-site has bios for five physicists who will feature prominently in the film: three theorists well-known for their work on large extra-dimensional models, one experimentalist from CMS, and one from ATLAS. The ATLAS experimentalist is described as “a leader in the search for extra dimensions.” I can’t find anything about the Higgs on the web-site, maybe they’ve already given up on that and left it to the Tevatron…

The descriptions of the theorists include “responsible for some of the wildest theories about the nature of gravity, cosmology and fundamental particles”, “a leader in the fields of supersymmetry, extra dimensions and new forces… has become a controversial figure by questioning experimentalists’ traditional methods of analyzing the data” and “the most likely to win a Nobel Prize after the LHC data is interpreted.” The experimentalist description is rather more modest (“has been involved in detector R&D and construction, software development and physics data analysis”), nothing about any possible Nobel prizes. If you had to choose whether to be a theorist or an experimentalist, the choice looks easy.

Steven Weinberg has a new preprint out entitled Living with Infinities, which is the written version of a recent talk given in memory of Gunnar Källén. Källén was a Swedish mathematical physicist, who died in a plane accident in 1968 at the age of 42. For more about him, see this by Ray Streater.

Weinberg begins by recalling his first first trip to the Bohr Institute in 1954, where he met Källén, who suggested a research problem involving an exactly solvable QFT model invented by TD Lee. The solvability of this model made it possible to use it for investigating renormalization outside of perturbation theory. Källén and Pauli showed that the model was non-unitary, Weinberg showed that it had states with complex energies.

In his talk, Weinberg describes Källén’s work during the 1950s investigating the question of how QED gets renormalized, outside the context of perturbation theory. Källén found an argument showing that at least one of the renormalization constants must be infinite but Weinberg notes that Källén never claimed the argument was rigorous, and concludes: “As far as I know, this issue has never been settled.” He goes on to give the now conventional Wilsonian description of the non-perturbative situation and the possibility that no non-trivial continuum limit exists. This question is now considered somewhat academic, since it is assumed that QED gets unified with other interactions and ultimately with gravity at energies below those at which the behavior of the coupling becomes problematic.

Weinberg states in his abstract that he will present his personal view on how the problem of infinities may ultimately be resolved. Here’s what he has to say about this:

My own view is that all of the successful field theories of which we are so proud — electrodynamics, the electroweak theory, quantum chromodynamics, and even General Relativity — are in truth effective field theories, only with a much larger characteristic energy, something like the Planck energy….

None of the renormalizable versions of these theories really describes nature at very high energy, where the non-renormalizable terms in the theory are not suppressed. From this point of view, the fact that General Relativity is not renormalizable in the Dyson sense is no more (or less) of a fundamental problem than the fact that non-renormalizable terms are present along with the usual renormalizable terms of the Standard Model. All of these theories lose their predictive power at a sufficiently high energy. The challenge for the future is to find the final underlying theory, to which the effective field theories of the standard model and General Relativity are low-energy approximations.
It is possible and perhaps likely that the ingredients of the underlying theory are not the quark and lepton and gauge boson fields of the Standard Model, but something quite different, such as a string theory. After all, as it has turned out, the ingredients of our modern theory of strong interactions are not the nucleon and pion fields of Källén’s time, but quark and gluon fields, with an effective field theory of nucleon and pion fields useful only as a low-energy approximation.
But there is another possibility. The underlying theory may be an ordinary quantum field theory, including fields for gravitation and the ingredients of the Standard Model…

He then goes on to describe the “asymptotic safety” scenario where the renormalized couplings approach a non-trivial fixed point as the energy cut-off is taken to infinity, a fixed point which presumably cannot be studied in perturbation theory, writing:

Other techniques such as dimensional continuation, 1/N expansions, and lattice quantization have provided increasing evidence that gravitation may be part of an asymptotically safe theory.

and referring to papers by Reuter/Saueressig, Percacci, and Litim (Percacci has a web-page about asymptotic safety here). He ends with the conclusion that, since string theory might not have any role in a fundamental theory, with only QFT needed to understand quantum gravity:

So it is just possible that we may be closer to the final underlying theory than is usually thought.

In these days of string landscape ideology, this possibility is an important one to keep in mind.

Lots of wonderful blog postings about math and physics out there worth reading, with a small sample including these:

From CERN, here’s a report from JoAnne Hewett about the summary session discussing the Chamonix workshop on the state of the LHC and plans for getting it up and running. The current schedule, which is tight, has collisions starting in November of this year, and running for nearly a year until late 2010. To accumulate an amount of data that would allow some significant new results (about 50pb^-1) should take six months or so, until mid-2010. The hope is to get to 2-300 pb^-1 later in 2010 before shutting down. This would not allow the LHC to do better than the Tevatron on the Higgs. For that, we’ll probably have to wait for data from the 2011 run. By the time this data is in, the Tevatron should have about 10fb^-1 to analyze, and may already have seen evidence of the Higgs.

Also at CERN, there has recently been a conference on the topic From the LHC to a future collider. Lots of interesting talks about future possiblities, including the ILC, CLIC, colliding LHC protons with electrons, as well as the possibility of a muon collider.

More and more areas of mathematics have a blog, here’s one for motivic homotopy.

Bert Schroer has updated two of his long articles that discuss both the sociology and conceptual framework of quantum string theory: String theory deconstructed, is dedicated to Philip Anderson and has a new section about history of the subject in Germany, and String theory and the crisis of particle physics, which is dedicated to Juergen Ehlers.

I hadn’t realized that Physics World has a blog. Among the latest entries are two reports (here and here) about Lenny Susskind’s recent talk to 700 people in Bristol about Darwin and the Cosmic Landscape. Susskind is still at it selling string theory and the multiverse to the public, no matter how unconvinced his colleagues may be:

Just as there is a vast landscape of biological designs, our best theories of physics imply an equally vast landscape of universe designs. String theory provides an analogue of DNA for the universe and modern cosmology makes use of a principle of mutation that creates a tremendously large multiverse.

It seems that

The central tenet of Susskind’s talk was that string theorists should look to Darwin because he “set the standard for what an explanation should be like”.

Funny, I always thought it was physics itself which set such a standard for the biological sciences, but I guess the idea now is to give up on that and have them be the gold standard.

While many theoretical physicists in their later years try and go for the Einstein look, according to one of the Physics World bloggers, Susskind is doing a good job of looking like Darwin.

I was recently looking up references about the history of Yang-Mills theory in order to write about it here, and one thing I ran into was the Wikipedia entry for Yang-Mills theory. It has three sections, the first two of which are standard material, but I was surprised to notice that the last section is completely unconventional, promoting the ideas of Marco Frasca and referencing two of his papers. It was written by an anonymous “Pra1998”, who I’m guessing is Frasca himself.

I’ve never tried to edit Wikipedia entries before, but I thought it would be a good idea to remove this material, which is not the sort of thing that belongs there. My edit was immediately reversed. I tried again, justifying this in the discussion section, but the material is still there. At this point, I give up, lacking time to deal with this and any understanding of what mechanisms are available in Wikipedia to deal with such a situation.

Over the last few years I’ve been finding myself consulting Wikipedia entries more and more, especially ones on mathematics. The quality of the mathematics entries is often shockingly high. In the past if one ran into mention of some mathematical concept one didn’t know about, tracking down a readable account of it was often insanely difficult. Now, one can often just look it up in Wikipedia and find a well-written, concise explanation of just the sort needed. It’s a wonderful and incredibly valuable resource, and I’m mystified about how such a high quality is achieved and maintained. I hope the same mechanism, whatever it is, can work for the Yang-Mills entry.

These are dramatic times for news about the US HEP budget, with the FY2009, FY 2010 budgets and stimulus package all coming together at the same time. The final stimulus package was very favorable for DOE and NSF, providing an extra $1.6 billion for DOE science and $3 billion for NSF.

Today there’s a draft FY2009 budget out of Congress, news about it here from Adrian Cho at Science magazine. HEP at DOE was down in FY2008, at $721 million (after a $32 million supplemental appropriation). For FY2009, which is half over, the draft budget has $796 million. There should be stimulus package funding on top of that. A proposed FY2010 HEP budget is being presented to OMB this week, and the President’s FY2010 budget proposal to Congress should be released in April. In the same draft, NSF research will get an overall increase of $362 million to a total of $5.18 billion (see here).

Today HEPAP is meeting in Washington, with presentations starting to appear online here. There are no decisions yet about what the supplemental funds will be used for, but according to the slides the guiding principles are to accelerate ongoing construction projects and update labs, increase operations and support of experiments at user facilities like Fermilab, and fund “selected research programs”, minimizing commitments in out-years. A program to support graduate students and early career scientists is under discussion.

More from HEPAP and more details about the FY2009 budget should be available soon.

Update: An outline of the FY2010 budget proposal from the President is now available. The proposed NSF budget is $7.045 billion, an 8.5% increase from the recent FY2009 omnibus legislation. The $3 billion from the stimulus package is on top of this. No detailed numbers, but priorities listed include “substantial increases for NSF’s prestigious Graduate research Fellowship and Faculty Early Career Development programs.” and increased “support for promising, but exploratory and high-risk research proposals that could fundamentally alter our understanding of nature, revolutionize fields of science, and lead to radically new technologies.” Sounds kind of like FQXI….

When learning about various ideas in mathematics and physics, I’m always fascinated by the history of these ideas and eagerly read whatever I can find on the subject. Partly this is because my understanding of ideas is often enlightened by finding out where they came from, especially what problems they were invented to solve. It’s also true that the history of these fields is a huge and remarkable story, in many ways far more intricate, subtle and surprising than any novel ever written, and can be appreciated as such. It’s quite possible that I’ve spent more time on this than is healthy, since there are good reasons for the fact that many scientists wait until late in their career to develop serious historical interests. Time spent studying history is not time spent developing new ideas.

One peculiar aspect of the present state of particle theory is that our current best fundamental physical theory, the Standard Model, is getting so old that fewer and fewer active physicists have any first-hand knowledge of its history. To a large degree, this history spans just about exactly a quarter-century, from renormalized QED in 1948 to asymptotic freedom in 1973. Before 1948 all we had were first-order calculations in QED, by 1973 the full Standard Model was in place. Physicists who finished a Ph.D in 1973 are now in their early 60s and soon will be getting to retirement age. First-hand understanding of where the Standard Model came from is now not part of the background of particle physicists in the most active stage of their careers.

One reason I started thinking about this is a recent exchange in the comment section of the last posting, sparked by my referring parenthetically to the fact that Yang and Mills had developed Yang-Mills theory (in 1954) in the context of trying to describe the strong interactions. The SU(2) gauge theory they wrote down didn’t work for this purpose, since what was needed was an SU(3) theory of quark colors, something that had to await at least the discovery of quarks. The SU(2) gauge theory of isotopic spin they were considering ultimately did find a role in the electroweak part of the Standard model, but this idea got started only after the symmetry properties of the weak interactions became clear later in the 1950s. Schwinger and his student Glashow were among the first to work on this idea, with the correct theory not appearing until 1967 after the role of the Higgs mechanism was understood.

Anonymous commenter “H-I-G-G-S” reacted to my allusion to this history as follows:

You said “Actually, Yang-Mills theory was invented to describe part of the standard model (the strong interactions)”

Not true. Go back and read the original paper.

Well, I have read the original paper, as well as a lot of secondary literature about it. The paper begins with a discussion of the symmetry properties of the strong interactions of nucleons and pions, which was the main topic of the day in 1954, due to the large number of strongly interacting states being discovered at accelerators. Nothing about the weak interactions, which was a different topic, with the symmetry properties of such interactions not understood until a few years later.

I devoted a few minutes to Googling “Yang-Mills” and “history”, and turned up quotes from David Gross and Steven Weinberg explicitly stating that the strong interactions were the motivation for Yang and Mills and posted comments with those. It seems though that “H-I-G-G-S” is not satisfied with this, recently responding:

Perhaps Yang and Mills were hoping to develop a theory of the strong interactions. Perhaps not. Where is the evidence that they were? You don’t cite any statements from their actual paper. You don’t direct me to any historical documents where they were interviewed about their thoughts. If you did I would be happy to have a look and I might be convinced that this was indeed their motivation. Instead you argue by appeal to a higher authority, in this case Gross and Weinberg. Of course when they argue about the importance of string theory you do not agree with them, but when they support a point you like they are suddenly experts who cannot be disputed. Gross was 13 years old when the Yang-Mills paper was published. Why do you think he should know what they were thinking?

I had actually cited a relevant statement from the paper, but I’m not sure what if anything could possibly satisfy “H-I-G-G-S”. Perhaps there is a published interview where Yang makes the kind of explicit, unambiguous statement about his motivations that “H-I-G-G-S” requires and maybe someone with enough interest can dig this up. Since “H-I-G-G-S” insists on anonymity, all I know is that he or she is from a major metropolitan area home to major universities, and appears to be a particle theorist who has been around for a while, although not long enough to know much history. Despite this, he/she has rather definite ideas about what this history is, coupled with a steadfast skepticism about any information which might indicate these ideas don’t correspond to historical reality.

I don’t know to what extent the case of “H-I-G-G-S” reflects the general understanding of the historical roots of the Standard Model among active theorists working on trying to extend it. Much effort on this blog has been devoted to trying to puncture the historical narrative that has solidified over the last 25 years about the supposed march forward of such speculative ideas such as extra dimensions, supersymmetry and string theory. Perhaps it would also be a good idea to worry about misconceptions concerning the history of successful parts of the subject, as well as the unwillingness of many particle theorists to give up such misconceptions.

Update: Here are some suggestions for reading about the history of the Standard Model, ordered very roughly from more popular to more technical:

For the early history of gauge theory, there is

Last Friday at the KITP there was a celebration of Stanley Mandelstam’s 80th birthday, with talks available here, and some messages from other physicists here. Geoffrey Chew recalls how Berkeley hired Mandelstam away from Columbia, where no one was very interested in what he was doing, in 1958. The next year the same thing happened with Steven Weinberg…

Recently I’ve noticed two books on a narrow topic not of general interest, but perhaps of interest to readers of this blog: histories of US math departments. They are:

Perhaps of even more esoteric interest, later this year Princeton University Press will publish Mathematicians: An outer view of the inner world, a book of photographs of mathematicians by Mariana Cook. Some of the photographs are available at her web-site here.

Via Ars Mathematica: Fulton’s Algebraic Curves is available for free online. It’s a good place to start if you’re looking for a challenging introduction to algebraic geometry at the (quite) advanced undergraduate level.

Some wonderful expository pieces about areas of mathematics:

The AMS Notices has an article about the current state of every mathematician’s favorite tool: TeX.

Les Houches this year will have a summer school devoted to lattice gauge theory.

For the latest on the question of whether the Tevatron will manage to see the Higgs or rule it out, see excellent postings by Tommaso Dorigo here and here. The bottom line is that by the time the LHC has enough data to start saying something about the Higgs, the Tevatron experiments will have over 10fb^-1 of data to analyze, which may, if improvements in their analysis work out, give them a two-thirds chance of seeing the Higgs at 2 sigma level over the entire expected mass range, or a 50/50 chance of seeing it at 3 sigma level over a large range, including a small range just above the 114Gev LEP limit. The Tevatron may remain very competitive with the LHC for some signals far longer than people have been expecting. And, at least for the next 18 months, the US stimulus legislation may make Fermilab better funded than CERN for a change…

I fear I’ve been remiss about not reporting on the IHES Grothendieck conference that I attended a couple days of when I was in Paris last month. Luckily, there’s a new blog here with a report.

Protests and strikes in France over Sarkozy’s attacks on the French scientific research system continue, see an English language report here. Some people may have misunderstood my previous mention of this. While it’s not a topic I’m well-informed about, Sarkozy’s argument in favor of moving to something supposedly more American, featuring a market-based, no central government regulation ideology has an obvious problem if you’ve been reading the newspapers.

Update: Video of the IHES Grothendieck talks is available here.