Musings

It’s up to you …

Around the blogs:

• Matt continues his excellent review of Lattice Gauge Theory, with a post on the classic paper of Lepage and MacKenzie.
• Luboš blogs about the paper of Itzhaki and McGreevy that I discussed a while ago.
• Urs is musing abut the $n^3$ degrees of freedom in the low-energy theory on $n$ coincident M5-branes.

• Sean writes about his new paper with Jennie Chen, on an attempt to explain why the initial state of the universe was one of low-entropy.

  I haven’t read their paper yet, but the idea is that our universe originated as a thermal fluctuation in an ambient de Sitter space, which then inflated. Personally, I’m sceptical that quantum gravity in (eternal) de Sitter space makes sense. Tout court, while there are certainly metastable de-Sitter-like solutions, I don’t think eternal de Sitter space exists as a solution to String Theory. But an approach like that of Carroll and Chen certainly has the advantage that one is not immediately plunged into the tangled thicket of quantum cosmology. Those discussions never go anywhere because, sooner or later, someone mentions “the wave function of the universe,” the physics-equivalent of Godwin’s Law, and all rational discussion comes to an end.

I previously linked to Eminem’s searing new single, Mosh. Well, now the video has been released. Directed by Ian Inaba of Guerilla News Network, it take “shrill” to a whole new level.

Apparently, Mr. Mathers is seriously committed to Get-Out-the-Vote to “disarm this weapon of mass destruction that we call our president… for the present.” Amazing how 4 years of this Administration can turn even a bad-boy Rapper to Civics Lessons, albeit very, very angry ones.

It’s been a while since I did a post about Web-Design, so here goes.

First, a disclaimer: while I am a proud owner of Joe Clark’s book (one of the two books on Web-Design that I own), that hardly qualifies me an expert on accessibility; you will probably find better advice from more knowledgeable sources elsewhere.

Anyway, for a variety of reason, including the fact that this precipitously cuts down on comment spam, the comment entry form is absent from the individual archive pages of this blog. Rather, it’s on its own dynamically-generated page and you need to follow a link to get to it. And, for reasons both æsthetic and practical, I decided that the comment-entry page should appear in a popup window¹. The code I started with looked like this

<a href="..."
onclick="OpenComments(this.href); return false;"
title="Respond to comment by ...">Reply to this</a>

The OpenComments() function creates the popup window. This code degrades gracefully. If the user has Javascript disabled, following the link opens the comment-entry page in the current window.

That’s good, but it could be better. The onclick event handler only applies if the user is navigating with a mouse (or similar pointing device). What about users who, perhaps because of a disability, are using the keyboard (or similar device) for navigation? We can accommodate them, too, by adding an onkeypress event handler²

<a href="..."
onclick="OpenComments(this.href); return false;"
onkeypress="OpenComments(this.href); return false;"
title="Respond to comment by ...">Reply to this</a>

I’ve been using this code for a year and a half, with nary a complaint, but it does conceal a serious usability gotcha³.

Consider the following steps

1. Click on a “Reply to this” link, opening a comment-entry popup window.
2. Start filling out the comment-entry form.
3. Click on the main window, to bring it to the front.
4. Hit any key.

Since the “Reply to this” link in the main window still had focus, the onkeypress event handler interprets your hitting a key to be a request to reopen the comment-entry popup window. Poof! There goes the comment you were composing.

Oops!

I was certainly aware of the problem but, since none of my commenters ever complained, I never got around to thinking about how to fix it. Perhaps my commenters were too shy to point out the problem or perhaps it simply hasn’t affected them.

One of the endearing features of Luboš Motl is that he is not shy about such matters. When he encountered the bug, he promptly declared my comment system “unusable.” And that, finally, got me off my duff to fix it.

The fix is simple: make sure that, after creating the popup, you drop focus on the link

<a href="..."
onclick="OpenComments(this.href); this.blur(); return false;"
onkeypress="OpenComments(this.href); this.blur(); return false;"
title="Respond to comment by ...">Reply to this</a>

I’m gonna guess that this is almost alway the right thing to do when you use an onkeypress event handler. Not dropping focus will frequently lead to unexpected results.

Another Usability Glitch Remedied

While we’re on the subject of comment popups, there’s another usability issue with MovableType’s comment popups. They are all named “comments”

function OpenComments (c) {
    window.open(c,
                    'comments',
                    'width=480,height=480,scrollbars=yes,status=yes');
}

So, you pop open a comment-entry window, start typing a comment, switch to another window, surf for a bit, absent-mindedly click on a comment link, … and wipe out the comment you had been composing.

Oops!

Since MT doesn’t actually use the name to do any fancy window manipulation, let’s make the name unique

function OpenComments (c) {
    window.open(c,
                    Math.round(Math.random()*10000),
                    'width=600,height=480,scrollbars=yes,resizable=yes,status=yes');
}

Now our comment-entry windows won’t stomp on anyone elses, or vice-versa.

Sean Carroll and Luboš Motl have both written blog posts recently on the anthropic principle. I’ve touched on the subject in the past and I don’t have that much that I wish to add to my previous discussions.

But there is one pitfall of anthropic reasoning that — I believe — is behind a lot of people’s unease with the subject. It’s the propensity, if one is not very careful and self-critical, to lapse into telling anthropic “just-so” stories of the sort that permeate, say, the “discipline” of Evolutionary Psychology.

Take, for instance, the problem of baryon number violation. The observed lower limit on the proton lifetime is 20 orders of magnitude longer than the anthropic bound. The generic supersymmetric theory has dimension-4 baryon number violating operators and the coefficient, $\lambda$, of these operators must be highly suppressed, to satisfy the anthropic bound. To satisfy the observational bound, $\lambda$ must be 4 or 5 orders of magnitude smaller, still. In a theory with low-energy SUSY breaking, this means we need to explain why the vacuum has a (very nearly) exact R-parity symmetry ($\lambda\lt 10^{-13}$), even though the anthropic bound is only $\lambda\lt 10^{-8}$. Split supersymmetry ameliorates the puzzle by making both observational and anthropic bounds on $\lambda$ much weaker, but the 5 orders of magnitude discrepancy between them remains.

It was in this context that I hungrily fell on a suggestion by Nima Arkani-Hamed that the smallness of $\lambda$ might have a different anthropic explanation. An approximate R-parity means that the lightest superpartner is approximately stable. To furnish a dark matter candidate, it should have a lifetime comparable to the age of the universe. Plug in the numbers, and you get something surprisingly close to the observational bound on $\lambda$ in models of split supersymmetry.

Tada! The smallness of $\lambda$, and hence the observed proton longevity, is explained by the anthropic need for dark matter. Or it would be, if structure formation were utterly impossible in the absence of dark matter, and if an LSP were the only dark matter candidate available…

I hope he doesn’t mind my embarrassing him further, but Matthew Nobes has the first in (what I hope is) a series of posts in which he discusses some of the analytical tools of modern lattice gauge theory. A lot of the improvement in lattice gauge theory has come about not so much by “brute-force” going to finer lattices as from being smarter about our computations. The number of lattice sites scales like $a^{-4}$ so, even tremendous strides in the computer power available lets you cut the lattice spacing by only a relatively modest amount.

Instead, the big improvements have come from being “smarter” about what to compute. By comparing lattice perturbation theory to the continuum, and using the results to fine-tune the lattice action, one can minimize the effects of the discretization and get vastly improved results on the same “coarse” lattice.

1. In comparing lattice perturbation theory to the continuum, we are interested in comparing physical quantities at some distance scale, $L$, long compared to the lattice spacing, but still much shorter than the size of the box. We should take care to use a “renormalization group-improved” lattice perturbation theory, rather than expressing our answers in terms of “bare” coupling(s) in the lattice action. The RG-improved perturbation series is generally much more accurate than the naive one in the bare lattice coupling.
2. Moreover, we can make the RG flow converge faster to the continuum by working, not with the “naive” Wilson action, but with an “improved” lattice action, containing “higher derivative” interactions, with cleverly-chosen coefficients.

Choose the coefficients correctly, and the errors scale to zero much faster as $a/L\to 0$. Matthew’s one of the guys who figures out how to do this in practice.

Recall that we were worried about finite spacing errors in lattice field theory. As an example we were using a scalar field coupled to gluons. The basic action was $$\phi D^{2} \phi$$ and this has $a^2$ errors. I said that we could use $$\phi (D^2 + C a^2 D^4) \phi$$ to reduce these errors. Clearly this involves picking some value for $C$, but how do we do that?

It pays to remember what the lattice is doing for us. It’s cutting the theory off at the small distance $a$, or in momentum space at high energy/momentum. So the spacing errors are reflecting a problem with the high energy (short distance) part of the theory. Now way back at the start of the first post we noted that QCD is perturbative at high energy. So we ought to be able to correct for the spacing errors perturbativly, by matching our lattice theory to the continuum theory to some order in perturbation theory. We pick some scattering amplitude, and fiddle with $C$, order by order. Done properly, this lowers the spacing errors, at a modest performance cost.

To fix bugs, you need to know about them first. Discovering bugs in itex2MML is particularly tricky, since nobody actually wants to look at the gobbledygook that is its MathML output. If the result renders OK in Mozilla and passes the W3C Validator, one tends to assume that it’s correct. Even when it doesn’t render properly, half the time the problem a bug in Mozilla’s MathML rendering code, rather than a bug in itex2MML.

One of the nifty features of the MathPlayer plugin for IE/6 is that, unlike Mozilla, it does a crude, but effective, form of error-reporting. Whenever it encounters incorrect MathML syntax, it renders it as best it can, but then colours the result red.

It was thus that Grant Focas discovered a bug in itex2MML. A ‘unary’ minus sign was being converted to <mo lspace="thinthinmathspace" rspace="0em">-</mo> instead of the syntactically correct <mo lspace="verythinmathspace" rspace="0em">-</mo>. Many thanks to Grant and to the kind folks at DesignScience for bringing this to my attention.

I’ve fixed the problem in my itex2MML distribution, and anyone using the itexToMML plugin for MovableType, WordPress, B2Evolution, PyBloxsom or ecto should update their itex2MML executable to the latest version.

And I want to put out a request to all of you reading this blog or the String Coffee Table in IE/6+MathPlayer: if you see a snippet of mathematical text rendered in red, please let me know. Similarly, anyone reading in any MathML-enabled browser¹, please let me know if some equations don’t seem to render correctly.

There have been a several quiet additions to the blogroll recently. Most notable is the brand new blog of Luboš Motl. Luboš is also a sometime-contributor to the String Coffee Table and the omipresent moderator of sci.physics.strings. Whether you agree or disagree with him, he’s always entertaining to read, so it’s great to see that he’s found yet another outlet for his thoughts.

Another blog of note is by Matthew Nobes, a lattice gauge theorist, who’s currently a postdoc at Cornell.

Seems like this physicist-blogger thing might be going somewhere…¹

(Yes, it’s Politics Week, here at Musings. Please have patience with us while we vent.)

A controversy has erupted as to whether Bush was wearing a wire during the first Presidential Debate, last Thursday. Salon.com, the New York Times and the Washington Post have weighed in on the subject of the suspicious-looking rectangular bulge in his jacket, clearly visible on the CSPAN video feed of the debate.

Personally, I have no idea whether he was or was not wearing a wire that night. The White House’s carefully-worded non-denial denial certainly hasn’t helped clarify the matter. What I do know is this: Karl Rove would be crazy to allow Bush out in public without a wire.

After his incoherent debacle last Thursday, and his slightly less embarrassing performance Friday night, I am getting peeved. I want to know what Karl Rove has planned for the next four years, and I’m not going to stand for any more “equipment failures.”

With the electoral campaign heating up, I’m pleased to announce a new feature on the sidebar of this blog: the latest State-by-State poll results from The VoteMaster. A candidate needs 270 Electoral College votes (or 5 Supreme Court Justices) to win.

Since the margin of victory in many states is far less than 2σ, it’s more than a little dubious to assign a state to one or the other candidate, based on polls which fluctuate from day to day. A more detailed view can be garnered by perusing the information on the site.

Still, it’s helpful (or depressing, depending on the day) to see what would happen “if the election were held today.” The results are snarfed from Dietrich Ayala’s most excellent Web Service using the GetXML plugin.

I’ve blogged a bit about the resurgence of interest in cosmic strings, in the context of string theory. In the old days, it was hard to imagine that cosmic (fundamental) strings would have tensions much below the GUT scale. Recent understandings of compactifications with fluxes lead very naturally to strings with tensions much below the GUT scale. That’s exciting because such beasts might actually be observable (but, hopefully, not ruled out by existing CMB data).

Tom Kibble has a very nice review on cosmic strings, the current observational limits, and some intriguing observations of what may be gravitational lensing by an oscillating cosmic string, as well as some other candidates for cosmic string lensing. The string tension would seem to be about $G\mu \sim \text{few}\times 10^{-7}$, which would be consistent with bounds from WMAP:

where $\lambda$ is the intercommutation probability, $\lambda\lt 1$, and $B$ is the fraction of the CMB power spectrum due to cosmic strings, which certainly satisfies $B\lt 0.1$. There are some more stringent bounds that have been argued for recently, but Kibble does not seem to put much stock in them.

In the debate, Dick Cheney lambasted John Edwards for his spotty attendance record in the Senate:

Now, in my capacity as Vice President, I am the president of the Senate and the presiding officer. I’m up in the Senate most Tuesdays when they’re in session. The first time I ever met you was when you walked on the stage tonight.

As a gazillion bloggers instantly pointed out:

National Prayer Breakfast, February 1, 2001

Thank you. Thank you very much. Congressman Watts, Senator Edwards, friends from across America and distinguished visitors to our country from all over the world …

Evidently, the old codger has grown senile. Could it be time to put him out to pasture?

Update: “If it’s Tuesday, this must be …” Edition

Apparently, Cheney can’t remember where he spends his Tuesdays either. Of the 127 Tuesdays on which the Senate was in session, he was present for only two.

I suppose this might come down to a matter of semantics. As a former president might have remarked, “It all depends on what the meaning of ‘most’ is.”

$$\mu \frac{d g}{d\mu} = - \frac{g^3}{48\pi^2} \left( 11 l(A) - 2 l(R_f) - l(R_s) \right)$$ It’s about friggin' time…

Whenever this blog comes up in conversation with another physicist, the first question I’m invariably asked is, “How many readers do you have?” Considering the sometimes excruciatingly technical, but always exquisitely dull nature of the content here, it would seem unlikely for that number to break out of the double digits.

My web-design/web-standards friends are typically curious about the breakdown of browser usage. As this blog is the poster-child for XHTML and advanced browser support for Web Standards, they’re curious to hear whether MSIE’s redoubtable dominance among browsers is diminished when you’re serving up MathML, and suchlike advanced content, that MSIE doesn’t handle¹.

It’s been a year since I published some browser statistics, so perhaps it’s time for another look. I looked at two samples for the month of September:

1. All visitors.
2. Visitors who came in via Google searches. The statistics for this latter, and hopefully more representative sample² of the browsing public are indicated in parentheses.

As before I excluded, as best I could, robots and other junk³. HTML page views have more than doubled since last year. Part of the increase⁴ is because I’m now hosting a second blog, the String Coffee Table here on golem.

Last year, MSIE and Mozilla were neck-and-neck in popularity in the overall sample, but MSIE beat Mozilla by more than 5-1 in the Google-search sample. With our larger audience, Mozilla has lost ground in the overall sample, but gained significantly — nearly doubled its share — in the Google-search sample:

I don’t know whether to be pleased or dismayed by the adoption rate of the MathPlayer plugin. On the one hand, we have more MathPlayer readers than Safari readers. On the other, they still comprise a paltry 14% of the total MSIE readership. It may be that those who want to see the equations switch to Mozilla and that those still using MSIE simply don’t care.

As you’d expect, the penetration of MathPlayer in the Google-search population is negligible.

Another interesting statistic is what operating systems visitors are using.

Among the Google-search population, the percentages have not changed significantly from a year ago. In the overall sample, Linux (almost all the Unix systems in these samples are running Linux) lost ground to Windows, while MacOS stayed steady. It’s probably more sensible, though, to think about these latter numbers in absolute, rather than relative terms: the number of our Linux readers remained constant, while the number of Windows (and MSIE) readers grew 2.5-fold and the number of MacOS readers doubled.

I suspect this may say more about trends in our readership than about trends in OS usage.

Dang! I forgot to mention that Itzhaki and McGreevy have a radically different spacetime interpretation of the large-N model of fermions in a harmonic oscillator potential, discussed in my previous post.

Just as the model of N fermions in the inverted harmonic oscillator potential is dual to the 1+1-dimensional noncritical string theory (the 0B noncritical string theory, to be precise), the theory in an uninverted harmonic oscillator potential can also be interpreted in terms of a weird sort of noncritical string theory.

In their version, the string theory has an unbroken spatial translation-invariance (and the Hamiltonian of the quantum mechanics problem is the generator of these spatial translations). The dilaton gradient is in the time-direction which, moreover, is compact. The string coupling is a pure phase, $g_s\sim e^{2i\phi}$, but the genus expansion is really controlled by $1/\mu_0$, where $\mu_0$ is the coefficient of the Liouville term, $\mu_0 e^{2i\phi}$ in the worldsheet Lagrangian.

What, you ask, is the physics of world where every point in space lies on a closed timelike curve? Well, their universe has two ends, at $x=\pm\infty$. If you fix the boundary conditions at $x=-\infty$, you can ask for the probabilities for different things to appear on the other boundary, at $x=+\infty$.

At least, that’s their interpretation of the physics when the filled Fermi sea has the topology of a disk. I have no idea how they would interpret the configurations which involve disconnected droplets, concentric rings, or whatever, each of which have quite elegant interpretations in AdS/CFT.

Anyway, if you think that this interpretation of the large-N gauged harmonic oscillator is too contrived and baroque, you haven’t been hanging out here long enough.

A while ago, David Berenstein suggested a matrix model description of the 1/2-BPS sector of N=4 SYM. The idea is to pick a $U(1)\subset SU(4)_R$, generated by $J$ and the Hamiltonian

When reduced on $\mathbb{R}\times S^3$, this theory is equivalent to a gauged large-$N$ matrix model with a harmonic oscillator potential. The dynamics of the eigenvalues of the matrix model reduces to a theory of $N$ free fermions in a harmonic oscillator potential.

The ground state of AdS₅×S⁵ is the filled Fermi sea, a circular disk in phase space. Ripples on the Fermi surface correspond to 1/2-BPS supergravity excitations ($J\ll N$). Isolated droplets above or holes below the Fermi surface correspond to giant gravitons ($J\sim N$).

Lin, Lunin and Maldacena have a very beautiful recent paper, in which they extend this picture to arbitrary droplets ($J\sim N^2$). They provide a detailed map between states of the Fermi theory and IIB supergravity geometries with $SO(4)\times SO(4)\times \mathbb{R}$ isometry and 16 supercharges. The supergravity solutions are specified by a function $z(x_1,x_2,y)$, obeying

The corresponding supergravity solution is nonsingular, provided $z(x_1,x_2,0)=\pm 1/2$. So we need to specify, as a boundary condition at $y=0$, those regions in the $x_1$-$x_2$ plane where $z=+1/2$ and those where $z=-1/2$. Equivalently, we specify the boundary between these two regions — a shape for the Fermi surface.

The topology of the Fermi surface determines the topology of the supergravity solution; the detailed geometry of the Fermi surface determines the geometry of the supergravity solution.

LL&M extend this prescription to compactifications of M-theory on AdS₄×S⁷ and AdS₇×S⁴. Really nice stuff.