Wednesday, September 17, 2008

Anti-Crackpot Blog

There is a new physics blog devoted exclusively to debunking the claims of crackpots (such as that the LHC will create black dragonsholes that will devour the earth). I'm glad somebody is doing this.

Wednesday, September 10, 2008

LHC online

As you probably already know, the LHC went online today with the first beam circulating. CERN has video (which unfortunately didn't work for me due to lack of the right plugin), and there are several liveblogs at Resonaances, Superweak, Cosmic Variance and the US/LHC blog.

Thursday, July 24, 2008

Lattice 2008, Day six

Saturday was the last day of the conference. The first plenary, chaired by Andreas Kronfeld, was devoted to the quest for new physics. Luca Silvestrini spoke about the observed discrepancies between lattice and experiment: A 4.4σ difference in the CP asymmetries in B to K π decays, a 3.8σ difference in fDs, and a 3σ difference in the phase of the Bs to J/ψ φ decay. Although the LHC is expected to give access to the low-lying part of the particle spectrum of the expected new physics, a Super-B factory will be needed to map the new physics out in detail (the MSSM has 160 parameters). Lattice QCD determinations of quantities of interest at the <1% accuracy level will be needed for these purposes.

Then George Fleming spoke about strong interactions beyond the Standard Model, where technicolor is making a comeback, since only some QCD-like versions of it have been ruled out. The interest in this area centers on "walking" theories with a very slowly running coupling. For SU(3), it is believed that there is a "conformal window" of Nf, where the coupling runs to an IR fixed point in the infrared. Simulations using unrooted staggered fermions to simulate Nf=4,8,12,16 indicate that this window lies somewhere around Nf=12.

The last plenary had Michael Teper speaking about Large-N QCD using old-fashioned OHP slides. N=&infinity; QCD is a theoretical laboratory for ideas about QCD, both because it turns out that as far as the N-dependence of observables is concerned, N=3 is close to N=&infinity;, and because at N=&infinity;, quenched QCD is full QCD, because fermion loops are infinitely suppressed by their colour factors; also, resonances become infinitely narrow as N goes towards infinity, allowing accurate measurements of e.g. the ρ mass, which turn out to be quite close to the real world at N=&infinity;.

This was followed by Hermann Krebs's talk about nuclear effective theories on the lattice. The lattice as a regulator is of course not unique to gauge theories, and nuclear theorists are now performing simulations of effective theories of pions and nucleons to determine the properties of light nuclei and nuclear matter from first principles. The low-energy constants can be either fitted to experiment by giving up an a number of predictions, or can be taken from lattice QCD (once they are determined accurately enough) for a truly first-principles treatment of nuclear physics.

After the end of the session, there was an announcement of the Les Houches Summer School on Lattice QCD in 2009. Then Kostas Orginos thanked the support staff and volunteers, before handing over to the representative of the Lattice 2009 organising committee, who thanked Kostas and his team. Everybody got their well-deserved applause, and then the lattice community was invited to come to Beijing for the Lattice 2009 conference, which is to be held July 26-31, 2009. It was also announced that Lattice 2010 will be held at a yet-to-be-determined location in Europe. And then the conference was over, and everybody said their goodbyes before leaving.

Since my flight only left the next day, I took the opportunity to visit the "Colonial Williamsburg" open-air museum, which I liked a lot better than the Jamestown one, largely because the colonials/locals just went quietly about their business without too much show or spectacle, which I thought gave one a much better impression of what life in the American colonies might have been like.

My flight back went fine, but I didn't get to post the last two summaries earlier.

Lattice 2008, Day five

Friday's first plenary started with a summary talk on heavy-flavour physics on the lattice given by Elvira Gamiz. The most striking point there is what is now being called the "fDs puzzle", i.e. the difference between lattice predictions (241(3) MeV [HPQCD Nf=2+1], 249(11) MeV [FNAL/MILC Nf=2+1], 244(4)(11) MeV [ETMC Nf=2 preliminary], 251(6)(?) [Alpha Nf=2 preliminary]) and experimental measurements (268(8)(4) MeV [CLEO-c, most recent]) of the Ds meson decay constant, for which new physics is being invoked as an explanation by many. Other topics were semileptonic decays of heavy mesons, which are quite hard to study on the lattice, and B-Bbar mixing parameters, where some also raise the possibility of new physics to explain discrepancies between theory and experiment that have recently arisen.

The next talk was Laurent Lellouch speaking about Kaon physics, and comparing the usefulness SU(2) and SU(3) chiral perturbation theory.

The second plenary session was started by Rob Pisarski speaking about heavy-ion collisions ar RHIC, where the study of the strongly interaction quark-gluon plasma (if it may be called that, since it does not really appear to be the state of matter formerly imagined under the name of quark-gluon plasma) requires methods from non-equilibrium thermodynamics and non-ideal hydrodynamics. One of the long-standing puzzles that appear to be experimental signatures of the QCD phase transition is the suppression of J/ψ final states and jets. Some explanation for these phenomena in terms of the "elliptic flow" of the quark-gluon plasma seems to have been found, but it appears to me that a fundamental undestanding of what is going on in these highly out-of-equilibrium situations involving strongly interacting matter is still a fair way off.

The next talk was related to this topic, as Harvey Meyer spoke about the extraction of hydrodynamical transport coefficients from the spectral functions of correlators of energy-momentum tensors, which requires some clever tricks to get the continuous spectral functions from the correlators measured only at a few discrete points.

After this, Yoshinobu Kuramashi gave a talk about PACS-CS's simulations of Nf=2+1 QCD at and near the physical pion mass. They were thus able to test the applicability of SU(2) and SU(3) chiral perturbation theory, and my interpretation of their results was that both might not be sufficiently well-behaved to be truly valid even at the physical point.

The last talk of the session was given by Tomoteru Yoshie, who gave an introduction and status update on the International Lattice Data Grid (ILDG), which now contains 183 ensembles with a total of 193,000 configurations using 41 Terabyte of storage space.

In the afternoon, there were again parallel sessions, including one in which Rainer Sommer spoke about our group's recent work on the Generalised Eigenvalue Problem for correlator matrices and how to use it in the most efficient manner to get ground and excited state masses and matrix elements, both in QCD and in effective theories such as HQET, and another on in which I talked about a preliminary analysis of Ds physics on the large and fine CLS lattices. Rainer's talk was certainly very well received, and since the potential criticisms of the work that I presented were easy to anticipate, I would say that my talk also went quite well.

Friday, July 18, 2008

Lattice 2008, Day four

Today was the customary short day. There were no plenaries, only parallel sessions. I went to the sessions on Standard Model parameters and renormalisation, where Peter Lepage presented the HPQCD collaboration's new method and results for the heavy quark masses from moments of current-current correlators, and after the cofee break the session on weak decays and matrix elements where Paul Mackenzie presented the Fermilab group's new result for fDs, which is larger than, but in agreement with, the HPQCD result, but at the moment has larger error bars than the latter. Notable talks in these sessions were also given by Ian Allison on results from high-β simulations and by Ruth van de Water on extracting an accurate number for |Vub| from QCD simulations by making use of variable transformations and complex fitting procedures.

After the end of the last session, we picked up our boxed lunches at the reception desk and climbed into the busses that took us to Jamestown settlement, where we got a tour of the museum, where the most remarkable exhibit were watercolours by John White, an artist who accompanied an early expedition to Virginia and depicted the flora, fauna and native population as they appeared to an English artist encountering the New World for the first time, while everything else was certainly informational and presented very nicely, but nothing unusual compared to the other historical museums. The reconstructed settlement was a bit too Disneylandish for my taste -- while the ships and buildings certainly gave a good idea of life in an early English colony in North America, the costumed show was more funny than informational, although I am sure the kids who were there were having a lot of fun, which is probably the main purpose of these kinds of reenactments. After that, the busses took us to the historical site of Jamestown, where we could see the ruins of the buildings and the rebuilt church and walk around in the heat until the busses took us back.

The banquet was a buffet dinner in one of the big rooms that can be divided to serve as three meeting rooms each. The menu is likely of no interest to readers, so I'll end here for today.

Thursday, July 17, 2008

Lattice 2008, Day three

Today's first plenary, chaired by Rainer Sommer, started off with the much-anticipated plenary talk about the state of dynamical fermion simulations given by Karl Jansen. Simulations with dynamical fermions are of course a hugely controversial subject in the community at the moment, with each group fiercely defending its particular fermion discretisation as the best, or even the only way to solve QCD (whatever that may mean). Karl managed to navigate this minefield (or to stay closer to the analogies he had chosen for his talk, this swamp of alligators) with great impartiality and fairness, pointing out the strengths and potential weaknesses of each formulation in an accurate and diplomatic manner; even regarding the great staggered controversy, he was very fair to both sides, pointing out that the concerns raised by Mike Creutz almost certainly don't affect the simulations being done now, given that they are being performed at fermion masses which are safe with regard to maintaining the order of the continuum (first) and chiral (second) limits, but that these concerns are also valid and worthy of further investigation in the context of theoretical studies in which the order of the limits is intentionally violated. A very nice picture shown was the scaling of the nucleon mass in different lattice fermion formulations, which looked like great evidence of universality; unfortunately, the same picture for the pion decay constant looked a lot worse, possibly because some formulations with ZA not equal to one may have used incorrect value of ZA. The progress made on reducing the cost of dynamical fermion simulations through algorithmic improvements (especially deflation) is also very impressive.

The next talk was Shoji Hashimoto speaking about simulations with dynamical overlap fermions. The overlap operator being the most expensive to simulate formulation of lattice fermions, the lattices being simulated are still pretty small, but it is nevertheless quite impressive that this has become possible at all.

After the coffee break, Ami Katz gave the non-QCD theory plenary talk, about AdS/QCD models. The AdS/CFT correspondence is maybe the most important (some might say the only) result coming out of string theory; as far as I understand it, it states that string theory in anti-de Sitter (AdS) space is dual in an apparently well-defined way to Large-N super-Yang-Mills theory on the boundary of AdS. A consequence of this appears to be that by introducing extended objects such as branes or black holes into AdS one can break the conformal symmetry or supersymmetry of the theory on the boundary, thus potentially being able to construct a supergravity theory that is dual to QCD. Since the AdS/CFT duality relates weak and strong coupling, this would allow to describe the low-energy spectrum of QCD by perturbative calculations in the dual theory. Some models that attempt to do this have achieved quite reasonable agreement with QCD spectra, but none of them are truly dual to QCD, so all of this amounts to model-building. I may well have misunderstood some things here, though, and corrections or better explanations in the comments are greatly appreciated.

The last plenary talk of the morning was Ken-Ichi Ishikawa talking about recent devlopments in the algorithms and machines field, such as the Cell processor, lattice QCD running on graphics cards, deflation and adaptive multi-grid methods for lattice QCD. His projections for the future seemed a little off, though: I am currently responsible for running a simulation which according to his final slides would require Petaflop computing.

After lunch, I attended the parallel session on hadron spectroscopy in which the different collaborations presented results on heavy-quark states. Christine Davies presented the HPQCD results on pseudoscalar decay constants, among which the result for fDs is remarkable for showing a 3σ deviation from the experimental value, which some believe is a possible sign of new physics.

After the afternoon coffee break, there was a public lecture by Rajan Gupta on the global energy problems facing the human species in the 21st century. The numbers are always very depressing, as is the political cloud of war, imperialism, famine and general oppression surrounding the fossile and nuclear energy resources of our planet. As a little contribution towards improving the level of discourse on energy issues he presented a project called OpenModel Global Obervatory that aims to create a Wikipedia-like database of the global energy infrastructure as a tool for policymakers and an instrument of educating the public. The fact remains that if 8 billion people all are to live the American lifestyle including its (ab)use of non-renewable fossile ressources, the next generation is probably going to be the last to be able to enjoy any kind of lifestyle above the level of "poor, nasty, brutish and short", if at all, so huge advances in energy efficiency and the use of renewable energies (photovoltaic, solar-thermal, wind, hydro, tidal) will be absolutely crucial -- economically viable fusion power would also be nice, but appears unlikely to appear soon enough to help us very much.

In order to cheer ourselves up after considering this, some colleagues and I had a beer with our dinner and discussed the most cheerful topics we could think of (which included cannibalism, assisted suicide and homelessness).

Wednesday, July 16, 2008

Lattice 2008, Day two

Today was a long day, so this will be a short summary. Any typos and inaccuracies in content are to be blamed exclusively on the wine served during the poster session.

After another continental breakfast, the first plenary session of the daym chaired by John Negele, started with a talk by Marc Vanderhaegen about nucleon structure studies. This was this year's experimental talk, for which reason I find myself too ignorant to give a good summary of it; there were lots of plots of experimental results of observables such as the ratio of the electric to magnetic form factors of the proton (which appears to be quite different if measured by unpolarised or by polarised probes for reasons to do with two-photon exchanges), the generalised parton distributions of the nucleon, and the magnetic dipole moment of the Δ(1232) resonance (which is apparently very hard to measure, because the Δ decays strongly and hence is far too short-lived to measure its magnetic moment by the precession method that can be used for stable or quasi-stable particles).

Next was James Zanotti who gave an overview of the work that has been done on hadronic structure from the side of lattice QCD. Again there were lots of plots of the same quantities, this side from lattice simulations, but I have to freely admit that I am way too ignorant of hadronic structure studies to appreciate this work very well. A better summary of the progress in this area that might be given in the comments would be appreciated.

After the coffee break, the second plenary session of the morning continued with Martin Savage in the chair. The nuclear thread of the previous session was continued by Silas Beane speaking about Hadronic interactions and nuclear physics. This was probably the funniest talk I have ever heard at a lattice conference (it included inter alia a picture of a crying baby held by G.W. Bush, illustrating the exponential growth with time of noise in baryonic channels, and of a live rabbit being pulled from a top hat). Multi-hadron states are now being targetted by lattice simulations, but dealing with the noise will require petascale computing.

The final plenary talk of the day was by Colin Morningstar, who talked about studies of excited hadronic states. His talk concentrated almost exclusively on the very extensive work done in this area by his collaborators, who have indeed made some remarkable progress on this very difficult problem; however, there are also some other approaches to extracting information on excited states, which may well turn out to not be competitive with the variational method, but might still deserve a mention at least in this blog.

After lunch with some colleagues, taken at an Asian buffet place that was both better and much more reasonably priced than the university canteen, I attended parallel sessions. The more remarkable talks included Constantia Alexandrou presenting a new method to extract excited states, which seemed to work remarkably well given that it appeared to be largely a rather glorified form of uniform random search. Progress towards using the HISQ action for simulations with staggered quarks including dynamical charm was presented by Alexei Bazavov. Michael Clark spoke about adaptive multi-grid methods for QCD as potential competitors to deflation methods. A presentation an a new high-performance computing architecture was given by John Mucci, the CEO of SiCortex, the company producing it -- it sounded a bit like marketing, but if their computers really only use 200 W per 100 GFlops and can run with ordinary air-cooling that would be quite amazing.

Finally, the poster session closed the day. My poster on the determination of the O(Nfαsa2) improvement coefficients for the Lüscher-Weisz action with dynamical HISQ fermions appeared to be received quite well by its intended audience. The food was gone quickly, and the wine not much more slowly. By an amusing coincidence there was a poster from another group about pretty much exactly the same work as I am doing with people at Zeuthen at the moment.

Tuesday, July 15, 2008

Lattice 2008, Day one

Hello from the College of William and Mary in Williamsburg, Virginia, where I am at the Lattice 2008 conference.

After a continental breakfast that was provided by the conference in the central meeting room, and registration (where we got a very nice conference bag, probably better even than the excellent one from Tucson), the meeting started with the usual welcomes from the Vice-Provost of Research and the head of the physics department.

Then the first plenary session started with Frithjof Karsch in the chair. The first talk was by Carleton DeTar, who talked about developments in finite-temperature QCD on the lattice. A he pointed out, the Nτ=4 simulations that were still fairly standard in that area rather recently correspond to lattice spacings of about a=0.27 fm at T=180 MeV, so by today's standards they are unacceptably coarse. A point of contention in finite-temperature QCD is the nature of the phase transition; while it is generally agreed to be a crossover and not a real transition at the physical point, for massless Nf=2 QCD there are some who believe it to be first order, while most groups find it to be second order. The fact that the transition is a crossover at the physical point poses the problem of how to determine the critical temperature, since for a crossover there is no uniquely defined transition point. The observables used to study the critical temperature can be divided into confinement-type (such as Polyakov loops) and chiral-type (such as the chiral condensate). A chiral-type observable that has led to some uncertainty about the critical temperature is the chiral susceptibility, which can be understood as the integrated correlator of the chiral condensate. Since this needs to be renormalised, it picks up a mass dependence which makes it difficult to pin down its precise temperature-dependence, thus leading to systematic errors in the determination of the critical temperature from its peak. Other interesting points raised in this talk were the ongoing effort to try to extract information on the transport coefficients of the quark-gluon plasma from lattice simulations, and the observation that dimensional reduction seems to work surprisingly weel down to about T=1.5 Tc, which is really completely unexpected, since dimensional reduction is strictly a high-temperature effective theory.

After that, Shinji Ejiri spoke about lattice QCD at finite density, an area that is known to be very difficult since the fermionic determinant becomes complex if the chemical potential is non-zero, thus runining the probability interpretation of the path integral measure and making Monte Carlo simulations impossible without some groundbreaking new idea that has apparently not arrived yet.

The coffee break was followed by another plenary session, chaired by Richard Brower. The first speaker was Shailesh Chandrasekharan who spoke about the worldline approach to simulating lattice field theories as an alternative to cluster algorithms for scalar and fermionic models, with the possibility of extending it to gauge theories as a worldsheet approach.

The next talk was by Uwe-Jens Wiese who talked about lessons for QCD to be drawn from solid state physics. Various solid-state physics models, such as the Hubbard model on a hexagonal lattice, can be described in terms of effective theories strongly resembling chiral perturbation theory, which in term can be reduced to qunatum mechanical rotors, whose spectra are known analytically. A similar reduction can be performed for χPT, and the nucleon can be incorporated in that approach as a Dirac monopole contained inside the sphere on which the rotor degrees of freedom live.

The final talk of the morning was Andre Walker-Loud speaking about Heavy Baryon Chiral Perturbation Theory. The main message I took from this talk was that a totally unphysical straight line fit appears to describe the pion-mass dependence of the nucleon mass just as well as involved HBχPT calculations, which is somewhat disconcerting.

After lunch with some colleagues at the somewhat expensive university canteen, the afternoon saw me attending parallel sessions. The cookies in the coffee creak were very delicious and probably had way too many calories. I also finally finished my talk. That's it for today, stay tuned for more tomorrow.

Thursday, June 26, 2008

Lattice 2008 programme online

The plenary program and preliminary schedule for the Lattice 2008 conference are now online.

Update: Meanwhile, the parallel and poster programs are also available.

Wednesday, June 25, 2008

I'm still here (and now we can finally be sure the LHC won't change that)

Yes, I have been lazybusy doing research, which takes priority over blogging (after all the German taxpayer is giving me money to do research, not to blog, and I don't want to disappoint her too much). But I'm still here, and I fully intend to blog from the Lattice 2008 conference in Williamsburg.

Fortunately most of us will still be alive by then, and even by the time Lattice 2009 in Beijing comes around, since the LHC is unlikely to swallow us up into a black hole. Okay, that's not really news to anybody who knows any real physics at all, but still CERN felt the pressure from misinformed segments of the public was enough to warrant yet another safety report, which comes to the conclusion that

[t]here is no basis for any concerns about the consequences of new particles or forms of matter that could possibly be produced by the LHC.

This hardly surprising conclusion is based on the fact that the flux of cosmic rays at energies far exceeding the energy of the LHC is such that if stable black holes, strangelets, vacuum decay bubbles or other doomsdayons could be produced at the LHC, the solar system would have been completely converted into those doomsdayons a long time ago. Since the sun, the moon and, indeed, the earth still consist after billions of years of being bombarded by cosmic rays with energies many orders of magnitude above that of the LHC, the probability for creating doomsdayons must be very, very low. Or, as the LHC safety report nicely puts it,

the continued existence of the Earth and other astronomical bodies can be used to constrain or exclude speculations about possible new particles thatmight be produced by the LHC.

Not that that will stop the silly trial in Hawaii from going ahead, but since it appears to be scheduled to begin in 2009, the LHC will have been turned on by then, and the continued existence of the Earth will make the doomsdayonistas look pretty stupid on their day in court.

Sunday, May 18, 2008


So I've obviously been a really bad blogger recently, but I was quite busy. One of things I was doing was attending a workshop at the ECT* (not sure what's up with the star; I suppose ECTRNPARA was a little too long, so they used a shell wildcard) in Trento, Italy. The workshop was sort of a miniature version of the lattice conference, with representatives from all major collaborations talking about the state of the art in simulations with dynamical fermions. I briefly considered live-blogging it like I do with the lattice conferences, but in the end decided against it for various reasons. The ECT* is very nicely located in a historical villa a little outside of Trento itself; the meeting room is in the basement of a side building, though, so there is nothing to distract one from the talks. The workshop was very well organised, with hotels, meals and everything arranged in advance, so five stars to the organisers and ECT* staff for that.

Contentwise, the workshop brought few real surprises, but a lot of confirmation of the fact that dynamical fermion simulations are now pretty far advanced due to a combination of algorithmic advances and ever greater and faster parallel computers. To all but eliminate systematic errors, ultimately, one will need to simulate at small lattice spacings (0.04 fm, say), large volumes (5 fm, say) and at the physical light quark masses. At the moment, each major group is accomplishing at least one of these, with some approaching two out of the three. In three or four years at the latest, somebody will have an ensemble of configurations fulfilling all three. Given that lattice spacings this small, or quark masses anywhere in the vicinity of the physical point, were considered completely out of reach just three years ago, it is fair to say that the lattice has come a long way in a short time.

Some people will therefore sometime use phrases like "when we will have solved QCD", but great as that sounds one first needs to consider what solving QCD means. Even when we have predictions for the hadronic ground state mass spectrum with essentially zero systematic error, there will still be excited states, decay constants and widths, scattering lengths, form factors, multi-hadron states and potentials, and so forth coming from QCD, and many of these will likely require considerable effort in terms of new theoretical developments in order to make it viable to extract them from lattice simulations. So unless "solving QCD" means "computing the hadronic ground state mass spectrum", we won't solve it for a fair while to come. Which is good news, because otherwise I'd really have to start looking for a different job, and I actually like this one.

And of course then there is the often-mentioned possibility that the LHC might find evidence of technicolor or some other new strongly coupled physics at higher energies, putting lattice theorists at the cutting edge of the energy frontier. That sounds more like some kind of dream though.

I've also been doing other interesting things, but I'll save those for a different post. If everything goes as hoped for, there may also be an exciting guest post on this blog in the not too distant future.

Friday, March 28, 2008

The LHC is making waves

The LHC is making waves on the web already before it is even being switched on. A rather unusual concept of what experimentalists really care about has been featured in this comic, but it is interesting to know that there are people who are genuinely worried that the LHC might "give helicopters cancer" or even swallow up the entire solar system. Peter Steinberg at the US LHC blog has more about them, including a link to this fine example of paranoia in action -- or is it intentional misinformation, or maybe satire? Of course, a well-known thriller writer who likes to claim his fictions as truth has written about CERN as an antimatter factory potentially useful to therrorists looking for an antimatter bomb, so what wonder is it if some members of the woefully uninformed public are willing believe this kind of stuff? More effective outreach is clearly needed.

Thursday, February 21, 2008

Word on the arXiv

The arXiv have announced that they now support submissions of "Microsoft Word DOCX or other OOXML (Office Open XML) document[s]". While I am perfectly aware that high-energy physicists (or indeed any kind of physicists) are not the only users of the arXiv, and that usage of TeX is not terribly common outside the physics/mathematics field (though I know a few philosophers and economists, and even one historian, who were won over by the superior look of texts typeset in LaTeX), I find this a little worrying, especially given that the arXiv acknowledges support from the Microsoft Technical Computing Initiative. What worries me is the possibility that this might be the first step towards a less open information architecture at the arXiv, and by implication in the high-energy physics communications sector. Will Microsoft try to gain a foothold, leading to the eventual establishment of their "open" (not) formats as the only accepted submission and download format? One sincerely hopes not.

Thursday, February 14, 2008

arXiv catchup

I have been too lazybusy recently to blog anything. However, in the spirit of the day, I'd like to share a romantic little poem extolling the nonabelian nature of strong attraction:

Roses are red, violets are blue
quarks come in colours, and so does glue.

No, I won't give up physics and become a card designer for H$llm$rk, don't worry. But after softening your hearts with this touching verse, I'd like to blog about some rather old stuff, which I hope hasn't gone stale in the meantime.

One paper on the arXiv that struck me as interesting in the last couple of months was this paper by Jeffrey Mandula (of Coleman-Mandula No-Go fame), who discusses the consequences of Lüscher's nonlinear realisation of chiral symmetry for Ginsparg-Wilson fermions. We recall that this symmetry can be written in two inequivalent ways by putting the phase factor eiαγ5 either on the quark field ψ or its conjugate $$\bar{\psi}$$. The crucial fact that Mandula points out is that both of these are independent symmetries of the lattice theory, and they don't commute! Hence, we have to look for the symmetry algebra generated by them, which turns out to be infinite-dimensional. Hence the lattice symmetry has an infinite number of conserved currents, a structure quite different from the continuum theory. However, it would really appear that the differences between any two of these lattice currents are just lattice artifacts of order a or higher that should disappear in the continuum limit, if the latter is properly defined. So some of the objections that the paper raises are likely a lot less serious than stated (especially the non-locality exhibited for free overlap fermions [eq. (38)] goes away once one realises that the continuum limit must be taken with the negative mass s constant in lattice units), but it appears that Ginsparg-Wilson fermions may have their own set of problems beyond just being expensive to simulate. Any comments on this from Ginsparg-Wilson specialists would be of great interest.

Another interesting paper was this one by Mike Creutz who proposed a new fermion discretisation based on features of the electronic structure of graphene. Apparently the low electronic excitations of a grpahene layer are described by the massless Dirac equation, and a lattice model based on this (by reducing the links in one of the three graphene hexagonal directions to points, and rescaling eveything to make the lattice rectangular again) exploits this to achieve the minimum number (two) of doublers permitted in an conventional chiral lattice theory by the Nielsen-Ninomiya theorem, and this construction can be extended to four dimensions and gauged to get a lattice discretisation of QCD with two light quark flavours. This was quickly followed up by a similar proposal for a minimally-doubling quark action, and by this paper which shows that any minimally-doubling chiral lattice theory necessarily has to break either of the discrete symmetries P or T such that their product PT is broken; this allows the generation of additional (relevant) dimension 3 operators that have to be removed by fine-tuning, precluding the use of minimally-doubling chiral actions in practice (unless some additional non-standard symmetry should conspire to do that fine-tuning itself, a possibility hinted at in the conclusion).

Saturday, January 12, 2008

Spammers strike

My apologies to our readers for the very nasty spam post that headed this blog for the last few hours. Somehow a spammer managed to break into Matthew's unused Blogger account and used it to post his garbage (in giant bold italics). I have suspended Matthew's account from posting at this blog for the time being, and I hope that this will put an end to the spammers' incursion into this forum. Apologies to all offended parties again.