Musings

Ever since hep-th was founded in 1991 (or maybe a couple of years later, when it sprouted a web interface), people have talked about trying to overlay some sort of “discussion” or “commentary” layer. For understandable reasons, Paul Ginsparg has been reluctant to host any such endeavour at arxiv.org itself, wishing to maintain it purely as an e-print server.

Two and a half years ago, I started this blog, in the belief that weblogs (and weblogging software) could provide a distributed mechanism for such an overlay, without the implied endorsement and other drawbacks of a centralized service. Blogs, as you know, provide a wonderful sense of an interwoven, distributed conversation. But the missing ingredient was the ability to ‘plug into’ that conversation from the arXivs. How do you discover that I or some other physicist-blogger, has commented on a given paper?

The obvious answer is, of course … Trackbacks. I’d been intermittently bugging Ginsparg to implement Trackbacks on the arXivs for a couple of years, now. Finally, at Sidneyfest, he sidled up to me and said, “So, about this Trackback thing …”

I’m happy to report that my pestering has finally paid off. The arXiv abstract pages are now Trackback-enabled. At the bottom of every abstract page, you’ll find a link, “N trackbacks” (when N>0). Click on it, and you’ll get a list of weblog entries commenting on that paper.

So does that mean that every crackpot and trackback spammer on the internet can now get linked-to from the arXivs? Well, … no. Just as you need to be a registered author to submit papers, your weblog needs to be on an approved list, in order for your Trackbacks to appear. Going forward, the precise mechanism for getting on that list is yet to be determined. But, in the short term, the list of serious physicist-bloggers is short enough to handle by hand.

You know who you are …

We physicists use a lot of PDF.

It’s the primary means of distribution of papers at the arXivs. It’s what we use to distribute class notes to students. The NSF requires our proposals be produced in PDF, … Indeed, pretty much anything with mathematical content is authored in TeX, and turned into a PDF file.

Accessibility is not something we think a lot about. Until, that is, we run into some regulation (either Government or University) that mandates that the documents we produce be accessible to the blind or vision-impared. If you’re Australian or Canadian, you may already have run afoul of these demands.

Sooner or later, we all surely will …

Joe Clark to the rescue.

I won’t repeat all the main points of his article. Instead, what I want to concentrate on is mathematical text, and our PDF content-creation tools.

First of all, everyone is, or should be, using pdftex. There used to be issues with handling figures in pdftex. But that’s a thing of the past. And pdftex offers so many advantages over tex→dvips→ghostscript (hypertext links, bookmarks, alpha-transparency, …) that there’s really no good reason to use the latter.

One important feature for accessibility is “tagged PDF,” which was introduced with PDF 1.4. By default, pdftex outputs PDF 1.4, but it doesn’t produce tags. You can retrofit tags into PDF 1.4 documents using recent versions of Acrobat. But it would be better if pdftex had the ability to generate them natively¹.

Accessibility of equations is something Joe didn’t touch upon at all, though he did allude to the shortcomings in the rendering of XHTML+MathML as a reason why they’re not going to replace PDF for mathematical texts anytime soon. But, whatever else you may say about it, MathML is accessible, and there’s at least one tool out there that will read MathML equations aloud. (Design Science received an NSF Grant for this effort, so, US readers, don’t think your Government doesn’t care about the issue.)

What about equations in PDF? Well, that’s the subject of another, more recent NSF Grant. What they plan to do, apparently, is embed MathML in the PDF file, and use the same technology, that allows their MathPlayer plugin to read MathML on the web, to read the MathML embedded in the PDF file.

MathML embedded in PDF … will some future version of pdftex support this? I don’t know. Ask Hàn Thể Thành. If not, there’s a serious possibility that, someday, you will be reduced to using MathType in Microsoft Word to produce accessible mathematical (PDF) documents.

I’ve just gotten back from a visit to the University of Washington which is, currently, the mecca for applications of AdS/CFT to QCD. I’ve talked a bit about some of the applications to RHIC physics. But there are lots of other interesting recent developments.

I’ll probably talk some more about them in future posts but, for today, I thought I’d summarize a paper by Erlich, Katz, Son & Stephanov.

Rather than trying to find a string background whose near-horizon geometry is holographically dual to QCD, they take a “bottom-up” approach, introducing those fields in AdS₅ which couple to the observables they are interested in. To study the low-lying mesons of QCD, they introduce 5D $SU(N_f)_L\times SU(N_f)_R$ gauge fields, $A_{L,R}^a$ which couple to the corresponding currents, $\overline{q}\gamma_\mu \frac{1}{2}(1\pm\gamma_5)t^a q$, and a 5D scalar, $X^{\overline{\alpha}\beta}$, in the $(\overline{N}_f,N_f)$ representation of $SU(N_f)_R\times SU(N_f)_L$, which couples to the quark bilinear. The geometry is taken to be that of a slice of AdS₅, $$ds^2 = \frac{1}{z^2} (dz^2 + \eta_{\mu\nu} dx^\mu dx^\nu),\qquad 0\lt z\leq z_m$$ The wall at $z=z_m$ represents the effect of confinement. Normally, this is the location where the supergravity approximation breaks down (curvatures diverge, etc.), and we need a stringy completion of the geometry, involving some D-brane. In this crude model, the 4D gauge coupling doesn’t run at all, until we hit the “IR brane,” where we simply impose some boundary condition.

The action is

where $g_5$ is the 5D gauge coupling. The (negative) mass-squared of the field $X$ is determined by the relation $m^2 = \Delta(\Delta-4)$, and the (naïve) scaling dimension, $\Delta=3$, of the quark bilinear. The UV boundary condition on $X$ is given by $$\lim_{z\to 0} \frac{2}{z} X(z) = M$$ where $M$ is the quark mass matrix. The other “branch,” as usual, gives the expectation value of the quark bilinear, $\Sigma^{\overline{\alpha}\beta}=\langle\overline{q}_R^\alpha q_L^\beta\rangle$,

Assuming no explicit flavour symmetry breaking, $M= m_q 𝟙$, the condensate $\Sigma= \sigma 𝟙$. In principle, value of $\sigma$ is determined by solving the classical equations of motion, subject to the boundary conditions for $X$ on the IR brane. Instead of specifying those, they treat $\sigma$ as another free parameter, and solve the equations of motion, using (2) as the UV boundary condition. For the gauge fields, they take the simplest possible boundary conditions, $$F_L(z_m)=F_R(z_m)=0$$ on the IR brane.

All in all, the model has 4 free parameters, $g_5, z_m, m-q,$ and $\sigma$. $g_5$ is fixed by comparing the large-$q^2$ behaviour of the 2-point function of the vector current to that of perturbative QCD, $$\frac{1}{g_5^2} = \frac{N_c}{12\pi^2}$$ The remaining three parameters are fit to data.

Assuming $N_f=2$ and isospin symmetry, some obvious observable to look at are the masses of the lowest-lying mesons, $m_\pi,m_\rho,m_{A_1}$ (respectively, the lowest mass pseudoscalar, vector, and pseudovector mesons), the pion decay constant, $f_\pi$, and the corresponding weak decay constants $F_\rho$ and $F_{A_1}$. Finally, there’s the $\rho$-$\pi$ coupling, $g_{\rho\pi\pi}$. That’s 7 observables, and 3 adjustable parameters.

The model (1) incorporates the basic structure of chiral symmetry-breaking. So, without any dynamical insight, you might expect agreement at the 10-20% level. Remarkably, the best-fit for the 7 data points has an RMS error $$\varepsilon_{RMS} = \left(\textstyle{\frac{1}{n}}\sum_i(\delta O_i/O_i)^2\right)^{1/2}$$ (here, $n=4=$ the number of observables minus the number of input parameters and $\delta O/O$ is the fractional error in each observable) of 4%.

That’s quite a bit better than we would have expected. It seems that, even in this very crude approximation, AdS/CFT captures some nontrivial features of the dynamics of QCD.

Ever since the program came out, I’ve been bitching about what a pain it is to do equations in Keynote. There are a plethora of little utilities that let you type a LaTeX equation, render the result to PDF, and then drag the resulting PDF fragment into Keynote.

Many people, who’ve experienced the pain of trying to incorporate LaTeX equations into alternative presentation software, think that is the cat’s pajamas.

But I find it incredibly clumsy.

1. If you want to re-edit the PDF equation, you can’t. You ought to be able to just double-click on the equation, bringing up the equation-editor, type your changes, and resave it. Until now, none of the solutions I’d tried allowed for this.
2. There’s no good way to do inline equations. The PDF objects can’t be inserted into the “flow” of a Text object. There’s no way to get the baselines to automatically line up, and there’s no way to automatically leave the correct amount of horizontal space in the text to accommodate the equations.

At least for the first problem, I’m happy to say I’ve found a solution. You need to install the Keynote 2 Linkback Plugin, which allows external applications to edit objects in Keynote. Then you can use LaTeXit to create and, subsequently, manage the equations in a Keynote presentation.

Here’s an example of editing a display equation in Keynote. That was easy, wasn’t it?

Now look at the inline equation on the same slide. It was created by layering the PDF object on top of the Text object. I left the requisite space for the equation in the Text object by the crude contrivance of hitting the spacebar a few times. This screws up, if you re-edit the text or, for that matter, re-edit the equation.

The search for a useful solution continues …

They’re cut from 150 lb slabs of dough, hand-rolled, boiled in honey-water, tossed with either sesame or poppy seeds, and then baked on long pallets in a wood-fired oven. With a crisp crust and a chewy center, they have a hint of sweetness (remember the honey-water). They are, in short, the best bagels in the world. Nothing else even comes close¹.

When my parents were alive, every visit was accompanied by four or five dozen, carefully-wrapped and frozen. These went straight into the freezer, to be doled out sparingly, until the next visit. Since then, we (my wife, though born in Chicago, is as passionate about these bagels as I) have been bereft.

So you can imagine my excitement when I learned that the St. Viateur Bagel Bakery now has a mail-order business. For $31.50 CAN, they’ll send a box of six dozen, via next-day air. Bliss!

Alas, a quick email exchange with José² established that they only ship within Canada.

Lack of demand? The hassle of dealing with US Customs? Pressure from the New York Bagel lobby? Who knows why they won’t ship south of the border! Whatever the reason, I am, needless to say … crushed.

We physicists tend to use ordinary English words, like “energy” or “field” in unconventional, technical ways. Mostly — even to a layman — it is recognizable, from the context, when a word like “energy” is being used in its technical, rather than its colloquial sense.

But, as I was reminded recently, that’s not always true, and can lead to some confusion. In particular, the use of the adjective “naïve” differs significantly from its colloquial meaning. In physics, a “naïve calculation” is one that omits some important effect, or makes some unwarranted simplification that, when properly understood, may significantly change the answer.

Which, in turn, reminds me of one of my favourite book, Rudolf Peierls’s “Surprises in Theoretical Physics” (and its sequel, “More Surprises…”). It’s a compendium of examples from various branches of Physics, where the naïve calculation yields the wrong answer, followed by a lucid explanation of what went wrong, and how a correct calculation fixes the problem.

To give you a taste, here’s a summary of one of my favourite “surprises,” that I sometimes talk about when I teach E&M.

Why isn’t a free electron gas paramagnetic?

In a uniform magnetic field, the trajectories of electrons are helices, which project to circles, when projected to the plane perpendicular to the applied magnetic field. Let $v_\perp$ be the projected velocity. The radius of the circle is $$r = \frac{m v_\perp}{e B}$$ and the magnetic moment should be $e v_\perp r$, or $$\mu = \frac{m v_\perp^2}{B}$$ (If you want the magnetic susceptibility, you would multiply this by the number density of electrons.)

That was easy. But, after a moment’s reflection, you realize that it’s complete garbage. This answer is independent of the electron charge, and it’s inversely proportional to the strength of the magnetic field. So it diverges for $B\to 0$!

What went wrong?

One of the interesting talks I didn’t talk about in my posts about Strings 2005 was by Petr Hořava. Now that the paper is out, I should try to make amends.

Hořava and Keeler propose a “noncritical M-theory” which is the double scaling limit of a 2+1 dimensional nonrelativistic (spinless) fermion in an inverted 2D harmonic oscillator potential. The idea is that certain vacua of this theory correspond to the type 0A and 0B noncritical string theories in 1+1 dimensions.

The 0A theory is obtained as follows. Work in polar coordinates, and expand the fermion in creation and annihilation operators $$\{ a_q(\omega), a^\dagger_{q'}(\omega') \} = \delta_{q,q'} \delta(\omega-\omega')$$ where $q\in\mathbb{Z}$ is the angular momentum in the plane. They propose that the OA vacuum with RR charge, $q$, is obtained by taking the double-scaling limit $$N\to\infty,\qquad \varepsilon_F\to 0,\qquad N\varepsilon_F = \mu\, \text{fixed}$$ and filling the Fermi sea for angular momentum $q$

while leaving it empty for angular momentum $q'\neq q$. $$a_{q'}(\omega) |0A\rangle = 0, \forall\omega$$

The 0B vacuum is obtained by working in Cartesian coordinates, where the energies of the two (inverted) oscillators are separately conserved. Pick a particular value of $\omega_2$, and fill the Fermi sea for those oscillators with that value of $\omega_2$, while leaving the Fermi sea empty for other values of $\omega_2$.

Effectively, you reduce the 2D inverted harmonic oscillator to a 1D one, which is the 0B theory.

On the other hand, this 2+1 D Fermion theory has lots of other interesting vacua that one can contruct in a double scaling limit. Hořava and Keeler discuss some interesting examples.

In particular, the 2+1 dimensional “noncritical M-theory” vacuum arises from filling up the Fermi sea, as in (1), for all $q\in \mathbb{Z}$.

What’s not clear to me, once one has decided to admit states of the 2+1 D theory with rather peculiar normalizability properties, such as these, where one should stop.

For instance, nothing prevents me from considering an $n+1$ dimensional nonrelativistic spinless fermion in an $n$ dimensional inverted harmonic oscillator potential. In appropriate cylindrical or Cartesian coordinates, I would again recover the 1+1 dimensional 0A/0B string, by an obvious generalization of the above construction. But this theory would have yet-more “interesting” vacua.

Another paper, also featuring free fermions, just appeared. It was the subject of Vijay’s talk. I should try to say something about that one soon.

There’s a firestorm raging through the blogosphere.

It really is diagnostic of which part of the blogosphere you inhabit, whether you think the subject of the firestorm is

1. the President’s endorsement of Intelligent Design,
2. the Strings 2005 discussion panel’s vote on the Anthropic Principle,
3. or Apple’s incorporation of DRM into the MacOSX/Intel Kernel.

You may recall my previous bemoaning of the sorry intellectual state of contemporary American conservatism. I did, however, note that there were a couple of exceptions to the general pattern of cravenness and confusion among the right-wing thinkers and pundits interviewed on the subject of Evolution and Intelligent Design.

Charles Krauthammer and Richard Brookhiser said sensible things. And, now, Krauthammer has written an essay expanding on his response.

How many times do we have to rerun the Scopes “monkey trial”? There are gaps in science everywhere. Are we to fill them all with divinity? There were gaps in Newton’s universe. They were ultimately filled by Einstein’s revisions. There are gaps in Einstein’s universe, great chasms between it and quantum theory. Perhaps they are filled by God. Perhaps not. But it is certainly not science to merely declare it so.

To teach faith as science is to undermine the very idea of science, which is the acquisition of new knowledge through hypothesis, experimentation and evidence. To teach it as science is to encourage the supercilious caricature of America as a nation in the thrall of religious authority. To teach it as science is to discredit the welcome recent advances in permitting the public expression of religion. Faith can and should be proclaimed from every mountaintop and city square. But it has no place in science class. To impose it on the teaching of evolution is not just to invite ridicule but to earn it.

Bravo, Mr. Krauthammer! The weight of redeeming the intellectual respectability of American conservatism appears to rest on your shoulders. I hope you’re up to it.

If you look at this purely as a cynical political move, it will help in the heartlands and people of my ilk care a lot more about Iraq than about textbooks in Kansas.

The inimitable Kung Fu Monkey delivers the smackdown [via James Wolcott, who has his own choice words about the deluded cynicism of Krauthammer and his ilk].