Musings

As I mentioned previously, Paul Krugman is worried about the rise of the New American Plutocracy. If you wait long enough, the Plutocrats have kids, which poses some interesting inter-generational questions about upward mobility in our society.

There’s a lively (as always) discussion over at Brad DeLong’s blog, along with a reprint of Krugman’s op-ed piece.

The latest field-theoretic proof, by Cachazo, Douglas, Seiberg and Witten, of the Dijkgraaf-Vafa conjectures appeared last week. It follows Dijgraaf, Grisaru, Lam, Vafa and Zanon and Ferrari (which I discussed previously and which is, strangely, uncited by Cachazo et al).

There are many points of similarity between these papers — the Konishi anomaly, for instance, figures prominently in any of these derivations — but, as they say, the devil is in the details. After all, the “naive” field-theoretic argument for the result (as sketched in DV’s original paper) is surely wrong. The argument basically says: since we are computing a holomorphic quantity, we can localize the functional integral onto the constant modes of the chiral fields, i.e. we end up with a matrix integral to do.

This argument is surely wrong because

• it is dimension-independent, whereas the result we are interested in is peculiar to 4 dimensions, as it relies on confinement, chiral symmetry breaking, the Konishi anomaly, etc.
• it does not explain why only the planar diagrams contribute (at finite N!).

So a real proof must grapple with the subtleties that a more naive argument leaves out. One of the refreshing things about the present paper is that some of the simplest questions one might ask are finally given a satisfying answer.

Consider an N=1 supersymmetric U(N) gauge theory with a chiral multiplet in the adjoint and a superpotential W(Φ). Generically, the gauge symmetry is broken by the expectation-value of Φ to Π U(N_i), with Σ N_i=N. The chiral fields of the “low-energy” effective action are the gluino condensates, S_i= Tr λ_iλ_i, of the unbroken U(N_i) and w_iα, the gauge field strengths for the U(1) center of U(N_i). But this description is not invariant under the original U(N) gauge symmetry, so it’s not obvious how to relate these fields to the underlying microscopic description.

Cachazo et al find the correct formula in terms of the microscopic fields, and show that these operators obey some Ward identities which follow from a generalized version of the Konishi anomaly (generalizing rescalings, Φ → εΦ, to arbitrary holomorphic reparametrizations, Φ → f(Φ)).
These Ward identities look like nothing else but the Virasoro constraints of the Matrix Model, and, of course, this determines the form of the solution.

The method generalizes quite readily to theories with a “diagonal” U(1) gauge symmetry, under which all the fields are neutral (here, because we only have matter in the adjoint). Such theories have a “hidden”, nonlinearly realized N=2 supersymmetry, under which the photino transforms inhomogeneously. Under this symmetry, the low energy chiral fields transform as

δS_i=ε^α w_iα
δw_iα=N_iε_α

which, in turn, is a powerful constraint on the form of the low energy effective action.

A remotely exploitable buffer overflow has been found in Samba. The version shipping with Jaguar, Samba-2.2.3, is vulnerable. You should either install the latest version or turn off Windows FileSharing (if you had it enabled) until Apple comes out with a Security Update.

Judging by their turn-around time with BIND, that should be in about two weeks.

According to Jim Sherman, Abbot and Costello are in charge of the White House. You read it here first.

We’re leaving a performance of La Traviata, and the psychologist turns to me and says,

“Sorry, that opera was too much like my work.”
“ Really?” I ask, “Do you have a lot of clients dying of tuberculosis?”
“No,” she responds, “AIDS, Hepatitis-C, and cancer.”
“Too much drama, too much anguish, and way too much whining.” she continues.
“But they whine so much more melodically in the opera.” is all I can respond.

According to the new tool, GetContentSize, the main page of this blog is a whopping 30% “content”. I know… it seems like the percentage is actually lower than that.

Thanks to Ed Felten for the tip.

With the UN inspectors on their way to Iraq, war plans are temporarily on hold. What will this Administration do to occupy itself in the meantime? The economy is sooo boring!

I know! They can do a music video.

OK, perhaps I have missed the point of Easther, Greene, Jackson & Kabat, but I find it deeply puzzling. The intent, apparently, is to produce a modern (M-theory) counterpart to the old work of Brandenberger & Vafa ( Nucl. Phys. B316 (1989) 391).

The idea there was to imagine that space had the topology of T⁹. If we populate it with a gas of free strings, they will be wound around the cycles of the T⁹ with some Boltzmann-like distribution. Turning the coupling to gravity back on, we obtain a cosmology in which some of the dimensions (those with zero winding number) expand, while others stay small.

The idea was to explain why we see 3 large dimensions.

Easther et al update this story to consider M-theory 2-branes wrapped on T¹⁰. Actually, they consider only the latter half of the story — the cosmological solution in a sector with a fixed set of winding numbers.

But what’s puzzling is how the first part is supposed to go. There is no such thing as a gas of “free” M2-branes (for precisely the reasons that de Wit, Hoppe & Nicolai’s attempt (Nucl. Phys. B305 (1988) 545) to construct a world-volume theory of the M2-brane led, instead, to the Matrix description of all of M-theory). I don’t know how to do the thermodynamics of full-blown M-theory, so I don’t see how we’re supposed to “produce” the desired distribution of winding numbers.

Of course, if one of the dimensions is much smaller than all the rest, membranes wrapped around that dimension have much smaller effective tensions and dominate the thermodynamics. These guys (known as Type IIA strings) DO have a weakly-coupled description, and hence we can do their thermodynamics. But I don’t see how one might even get started in the general case.

Update: I’m even puzzled about the part of the story that they do try to tackle. Fix a total charge (set of wrapping numbers). At “late times”, as they would call it, you are dominated by the lowest-energy M2-brane configuration carrying that charge. I’m not sure they do that correctly.

Consider, as a baby example, strings wrapped on a rectangular T² with side lengths R₁,R₂. The charge is labelled by a pair of integers, (N₁,N₂). Naively, you might think that the lowest energy configuration with that charge has energy

N₁R₁+N₂R₂

(times the string tension). But that would be wrong. The lowest energy configuration has energy

k (p₁²R₁²+p₂²R₂²)^1/2

where k is the greatest common divisor of N₁ and N₁: (N₁,N₂) = (k p₁, k p₂).

Similar (though more complicated) formulae hold for higher dimensional tori and for the case of membranes wrapped on them. I could be wrong, but I think this makes a difference in their analysis.

So I find myself in Central New Jersey again, for Curt Callan’s 60^th birthday Festschrift. The weather sucks, but the talks have been great.

One of the striking things is just how far we have come since the dark days of the late 1960s, when quantum field theory was in disrepute, and no one had the slightest idea how to understand the strong interactions.

Equally striking was how quickly things fell into place, once people started looking at them the right way. Bjorken Scaling (confirmed, in short order, in deep-inelastic scattering experiments at SLAC), Wilson, Callan and Symanzik’s work on the Renormalization Group, asymptotic freedom and QCD all followed quickly.

String theory also had its roots in the late 60s, precisely as a non-field theoretic attempt to understand the strong interactions. It’s evolved considerably, but in many ways, we are faced with the same problem facing the high energy theorists of the 1960s. We appear to lack the intellectual tools to do the sort of computations we need to be able to do.

Of course, they had experiments to fall back on. In the case at hand, scaling in deep-inelastic scattering was the crucial clue. It meant that, at short distances, weakly-coupled field theory was relevant. Making sense of that remark was the key that unlocked all (or at least most of) the doors.

We, of course, don’t seem to be getting much help from experiment these days. That’s a pity, but what was really crucial then was this theoretical insight which picked up on the result of one experiment out of the myriad of data that was available.

The difficulty in finding a more fundamental formulation of string theory is imagining something that might reproduce the rich variety of phenomena we have found in string theory’s various limits. We need a similar “simplifying insight” today.

Gee, that’s far more philosophical than I intended to be in this post. Perhaps next time I’ll get back to discussing some actual physics.

One of the most talked-about new features of the new MacOSX 10.2.2 update is Apple’s implementation of Journalling for HFS+. Enabling journalling is as simple as

sudo diskutil enableJournal / 

What journalling is good for, and whether you should enable it are discussed in this nice article.

Yet another vulnerability has been found in the BIND DNS server. If you’ve enabled the NameServer on your machine (even as a caching-only nameserver), you had better upgrade to BIND 9.2.1.

And, either way, you’d better hope that your ISP has done the same…

Gary Shiu gave a lovely talk today about his work with Easther et al.

From the ensuing discussions, it was clear that Weinberg’s objection probably doesn’t apply. One would have to cook up a pretty screwball inflaton potential to mimic the effect that they predict.

I’ve been getting a lot of hits from people using the RadioUserland News Aggregator. I guess some people want to know the instant this blog is updated.

So here’s a plugin for MacReporter, the MacOSX dockling News Aggregator.

Just install it in “~/Library/Application Support/MacReporter/Plug-ins”, and select it to be active in the Plugin Preferences.

Update: I also built plugins for some of my favourite blogs. They’re available from the sidebar of the main or monthly index pages.

The much-anticipated New York Times article on the Bogdanov scandal has appeared. Alas, it suffers from the usual journalistic conceit that a proper newspaper article must cover a “controversy”. There must be two sides to the controversy, and the reporter’s job is to elicit quotes from both parties and present them side-by-side. Almost inevitably, this “balanced” approach sheds no light on the matter, and leaves the reader shaking his head, “There they go again…”

In this case, the two camps are the “It’s Obvious Nonsense” camp and the “It’s all Greek to Me” camp. The former are quoted as saying:

“One thing that seems pretty clear to me is that the Bogdanovs don’t know how to do physics.”
— John Baez

“… really empty”
— Carlo Rovelli

“I do think that the examiners, referees and editors do have something to answer for in this case,”
— Lee Smolin

“It is easy to judge, even from the abstract alone, that these papers are nutty,”
— David Gross

The latter said:

“…intriguing.”
“One person looks at a piece of art and says it is gibberish; another person looks and says it’s wonderful.”
— Roman Jackiw

“It’s a difficult subject, … The paper has a lot of the right buzz words.”
“This says something profound about what happens to theoretical physics in the absence of the discipline of experiment.” [I’ve debunked this latter argument elsewhere.]
— Frank Wilczek

“Scientifically, it’s clearly more or less complete nonsense, but these days that doesn’t much distinguish it from a lot of the rest of the literature.”
— Peter Woit

“What they did or what they have written seems to show that they are not better (but not worse) than several theoretical physicists friends of ours who often use some mathematical terminology that they do not master well enough.”
— Robert Coquereaux

As you can see, the “It’s all Greek to Me” camp is further subdivided (though the dividing line is rather fluid) into the “I’m not so sure it’s nonsense” and the “Maybe it’s nonsense, but so are most of the papers on hep-th” schools. Both are distinguished by a professed inability to tell sense from nonsense. The two schools differ only in whether the default assumption about papers they don’t understand (or haven’t read) is that they are sense or that they are nonsense.

Finally bit the bullet and upgraded my iBook to Jaguar. I had such a horrible time when I upgraded Golem, that I was a bit reluctant. Fortunately, it went much more smoothly the second time around (it helps to know all the glitches beforehand!).

The only major breakage was expected: my spreadsheet, Mesa.app, can’t print under Jaguar, and my fruitless dealings with the company have lead me to the conclusion that it ain’t never gonna work under Jaguar.

I guess I’ll be looking into MarinerCalc instead.

My biggest disappointment is that (short of ponying up for a .Mac subscription) there is no way to sync address book and calendars between the two machines. The technology (SyncML) is there. But, at least for me, iSync serves no useful function except to make me wish I had a Bluetooth phone.

Dang! Next, I’ll be wanting Bluetooth luggage as well.

In light of my previous entry, I thought a closer look at Danielsson’s paper on α-vacua was in order.

There are several objections to the proposal that the initial state of the inflaton be an α-vacuum.

• The Equivalence Principle: At length scales much shorter than the radius of curvature of de Sitter space, physics should be Minkowskian. But the α-vacua don’t approach the Minkowski vacuum at short distances.
  Danielsson’s response is that, if inflation starts not too long after the Planck time, then there are no length scales “much shorter than the radius of curvature of de Sitter space” at which effective field theory is valid.
• Acausal Singularities of the Green’s Functions: The Green’s functions in the α-vacuum have quite screwy behaviour outside the lightcone.
  But, responds Danielsson, “physical” Green’s functions, like commutators or retarded Green’s functions do vanish outside the lightcone, just like in Minkowski space. Even in Minkowski space, “unphysical” Green’s functions, like the Feynman propagator are nonvanishing outside the lightcone.
• Screwy Perturbation Theory: Similarly, says Danielsson, one might have thought that pertubation theory (loop amplitudes) was sick in an α-vacuum. But it isn’t.
• The Exit Problem:The Bunch-Davies vacuum matches onto the Minkowski vacuum when we exit from inflation. Of course we don’t want to end up precisely in the Minkowski vacuum; we want the universe to reheat. But we don’t want a boatload of ultra-energetic particles either.
  Here, I think, the response is less satisfactory. Danielsson argues that the effects may possibly evade the observational limits. But this is clearly still a big problem for the α-vacuum “scenario”.

Our favourite stoneudent makes the daily comics.

Update: And, yes, she was on Benadryl.

Pursuant to a thread in sci.astro.research Ted Bunn has posted three CMBR sky maps.

Two are computer-generated noise. One is actual raw COBE data. Can you tell which is which?

The Chronicle of Higher Education has a piece on the Bogdanov Affair.

Frank Wilczek (as bad luck would have it, Editor-in-Chief of Annals of Physics, one of the journals taken in by the Bogdanovs) is quoted as blaming the formal (divorced from experiment) character of much of high energy theory these days for the apparent difficulty in sussing them out.

I don’t buy it. I’ve yet to encounter anyone with a working knowledge of any of the fields (topological field theory, quantum groups, von Neumann algebras, …) touched on by the Bogdanov papers who had any difficulty deciding whether there was real content there.

If the referees were lazy, and accepted a paper they shouldn’t have, then let’s admit it and move on. We all know that it’s a lot less work to accept a paper than to reject it and then have to deal with the inevitable resubmission(s) from the authors. And, often, after a long, drawn-out battle, the authors will demand the opinion of a new referee who, to your chagrin, will go ahead and accept the paper anyway. The miracle, really, is that the percentage of crap papers accepted for publication is as low as it is.

The Editors of Classical and Quantum Gravity were forthright and 'fessed up. Wilczek should, too, rather than blaming some perceived defect of the field.

More serious, I think, are the PhD Advisor and Dissertation Committees who, apparently abdicated all responsibility for the contents of the dissertations.

But we still don’t really know the whole story of that aspect of the affair. The soap opera continues…

So, can one use measurements of the CMBR to detect the influence of high energy physics on the power-spectrum of primordial density fluctuations? Obviously, one crucial factor is the size of the corrections to the power spectrum induced by high energy physics at a scale Λ.

The usual calculation assumes as an initial condition that the inflaton field starts in the standard “Bunch-Davies” vacuum. But Danielsson and Easther et al have argued that a wider class of de Sitter-invariant vacua, the so-called α-vacua might plausibly be taken as initial conditions for the state of the inflaton field. If do, then the corrections to the power spectrum are of the order H/Λ, where H is the expansion rate at the time when a fluctuation of a given scale crosses out of the horizon.

The Stanford group have argued that it is problematic for the initial state of the inflaton field to be anything other than the Bunch-Davies vacuum. If they’re right, then the effect of high energy physics can only be encoded in higher dimension operators in the effective lagrangian for the inflaton, which lead to corrections of the order (H/Λ)². While they try to put a bold face on it, it seems highly unlikely we could ever measure such a small effect.

Recently, it seems that the argument has been swinging in favour of the α-vacuum guys. If so, the effect might be eminently measurable in the near future.

The fly in the ointment (as Steve Weinberg keeps emphasizing to me) is that, while it is true that the power spectrum of fluctuations as they leave the horizon depends only on the slope of the inflaton potential at that time, what we see today depends on the whole shape of the inflaton potential. With a variable-slope potential, we can get pretty much anything we want.

If Steve’s right, there’s not much that we can conclude from these observations.

I used to have a lot of respect for Andrew Sullivan.

But since he left the editorship of The New Republic, and started blogging full-time, his writing has gone precipitously downhill. It is now positively painful to read.

Fortunately, there is a smarter (OK, if not smarter, at least funnier) alternative out there. Enjoy!

Upgraded this blog to Movable Type 2.51. While the software has improved, the contents, alas, remain the same.

Many people have been hoping recently that observations of the cosmic microwave background might provide a “window” into high energy physics well beyond the energy scales accessible in terrestrial accelerators.

So far, however, a concrete (and detectable!) “signal” to look for has proven elusive.

Juan Maldacena has a really nice paper on the leading non-gaussian contributions to the fluctuations in a slow-roll inflationary model. He computes the 3-point functions of scalar and tensor fluctuations. The effect is order (H/M_pl)⁴, and so probably unobservably small.

Still, a nifty computation.

The Bogdanov story just gets weirder and weirder. The following details come from John Baez.

• Indeed, as I reported earlier, the Bogdanov brother were claiming to have PhDs in physics back in 1991 when they wrote their book Dieu et la Science. Unfortunately, the claim was false, and the book was plagiarized from The Secret Melody by Trinh Thuan, an astronomer at the University of Virginia. The fact that they had falsely claimed to have PhDs became an issue at the subsequent trial.
• At the time of the trial, they tried desperately, but unsuccessfully to get PhDs on the quick. That attempt was unsuccessful, but not long afterwards (1993), they started work at the Université de Bourgogne, and eventually, they did get their PhDs: Grichka in Math (June, 1999), and Igor in Physics (July, 2002).
• Dennis Overbye of the New York Times is looking into the case. I imagine the Science Times article which ensues with be a “keeper”.
• The Editorial Board of Classical and Quantum Gravity has taken the unusual step of issuing a statement expressing regret that the Bogdanov paper made it through their referee process, though it “does not meet the standards expected of articles in this journal.”

Ah, the French, the French…