Musings

Catch a very interesting discussion over at Cosmic Variance of a paper by Evans, Morris and Rosten, relating Morris’s Exact Renormalization Group for large-$N$ $SU(N)$ Yang Mills to the “Ghost D-brane” proposal of Okuda and Takayanagi.

The claim is that, by embedding $SU(N)$ Yang-Mills in a larger (nonunitary) theory, whose gauge groups is the supergroup $SU(N|N)$, spontaneously broken to $SU(N)\times SU(N)$, one can produce a gauge-invariant Pauli-Villars regulator, with which to implement the Exact RG. The latter theory, in turn, is what Okuda and Takyanagi argue is the world-volume theory of a stack of D-branes and ghost D-branes.

When the gauge symmetry is unbroken, the $SU(N|M)$ theory is equivalent to $SU(N-M)$, as far as computing gauge-invariant observables. In particular, there is a perfect cancellation of diagrams for $N=M$.

Turning on a nonzero Higgs VEV (separating the D-branes from the ghost D-branes) provides a cutoff for the original $SU(N)$ theory. Above the scale of the Higgs VEV, you get zero; far below it, the “original” $SU(N)$ degrees of freedom decouple from the ghost $SU(N)$.

Evans et al propose and AdS/CFT geometry realization of this idea, with the hope of connecting, in a explicit way, the “holographic RG” (evolution in the radial coordinate of AdS) with the “exact RG” of Morris.

Anyway, Takuya Okuda is over there, fielding questions, so take advantage …

I wasn’t going to post anything about the recent paper by Arkani-Hamed et al, figuring that Luboš is perfectly capable of explaining himself. But, after discussions with various people, it became clear that a few comments are in order.

They argue for two propositions which “must” be true in any theory of quantum gravity, but which are not obvious, at all, from the point of view of low-energy effective field theory. They both concern theories in which there is an unbroken $U(1)$ gauge symmetry in the low-energy theory.

First, they argue that there must exist charged particle(s) in the theory, whose charge-to-mass ratio exceeds¹ the extremal bound on the charge-to-mass ratio of blackholes. A-priori, you could imagine that one could twiddle the masses and charges of fundamental particles arbitrarily. However, as they make clear, in the absence of particles which exceed the bound, charged blackholes cannot radiate away all their charge, and one is left with a large (possibly infinite) number of charged remnants.

This is a perfectly solid result, and one which can be understood quite clearly, once one takes account of blackholes and their evaporation. From it, they abstract away the slogan, “Gravity is the weakest force.” Which leads them to their second conjecture.

The strength of the effective gravitational force grows like a power-law in the UV. The strength of gauge-interactions vary only logarithmically (growing in the UV for abelian gauge theories and falling in the UV for asymptotically-free nonabelian gauge theories). If we go to high enough energies, the gravitational force, therefore, comes to dominate, or would do so if the theory were not cut off.

If we ignore the slow logarithmic running of the gauge coupling, demanding that gauge-interactions dominate over gravitational ones puts a cutoff on effective field theory, not at $M_{\text{pl}}$, but at a lower scale, $g M_{\text{pl}}$.

Now, it’s certainly true in all known string theories, 4D effective field theory breaks down below (often, well below) the 4D Planck scale. Indeed, as Arkani-Hamed knows well, the scale at which 4D effective field theory breaks down could be as low as several TeV. I firmly believe (along with the authors) that this is a general principle. But, to put a precise upper bound on the cutoff, at which 4D effective field theory must break down, does require taking account of the running of the gauge coupling.

To sharpen the conjecture, the authors assert that “$g$” in the above formula is the low-energy value of the gauge coupling below the mass of the lightest charged particle. This is not directly related to the “high-energy” value of the coupling (close to the cutoff scale). The rate at which the coupling runs depends on massive charged species at intermediate scales. Not just the magnitude, but even the sign of the $\beta$-function could change (if the abelian gauge theory is un-higgsed into a nonabelian one). So the scale at which gravity and gauge interactions become comparable in strength cannot be determined from low-energy data alone; it could be higher or lower than the “naïve” estimate of $g_{\text{IR}}M_{\pl}$.

Indeed, in many string backgrounds, $SU(2)\times U(1)$ is unbroken, and the quarks and leptons are massless. (In the same approximation, supersymmetry is, frequently, also unbroken.) In that case, the $U(1)$ gauge coupling is driven all the way to zero in the IR². But that does not mean that effective field theory has zero range of validity.

One can imagine a self-consistent bound of the form $\Lambda = g(\Lambda) M_{\text{pl}}$. That’s the form of the bound that they actually check in examples. (It’s $g(\Lambda)$ that is directly related to $g_{\text{st}}$, not $g_{\text{IR}}$.) In that form, as they verify, the bound holds³. But it’s not a form that depends solely on low-energy data.

In my previous post, I argued that accesskey keyboard shortcuts, to be usable, need to be

1. discoverable
2. modifiable

and I suggested some techniques for achieving that. To make them discoverable, I suggested including on each page, in some artful way, a definition-list of the form

<dl id="AccessKeyList">
<dt>0</dt><dd><a href="/~distler/blog/accessibility.html" accesskey="0">Accessibility Statement</a></dd>
<dt>1</dt><dd>Main Page</dd>
<dt>2</dt><dd>Skip to Content</dd>
<dt>3</dt><dd>List of Posts</dd>
<dt>4</dt><dd>Search</dd>
<dt>p</dt><dd>Previous (individual/monthly archive page)</dd>
<dt>n</dt><dd>Next (individual/monthly archive page)</dd>
</dl>

with the accesskeys for your site. To make them modifiable, I proposed a Javascript, which turns that definition-list into a template for editing the keybindings, and stores your modified keybindings for future visits.

But what about all those millions of sites, with accesskeys defined, which haven’t gone to this trouble? Since Gez Lemon inspired me to write the above Javascript, it was my turn to inspire Gez. Firefox users can install this Greasemonkey script which provides an (admittedly slightly crude) approximation to the same functionality on any site with accesskeys.

Without an author-supplied definition-list, Gez’s script needs to guess at the meaning of each accesskey. Usually, that works passably well. But, on some sites, the result can be downright comical. Obviously, it would be better if website authors went to the trouble of providing the aforementioned definition list. And with the aforementioned Javascript, all their users (not just those with Firefox and Greasemonkey installed) could customize those keybindings.

But still, it’s remarkable that, with a little clever scripting, Firefox users can now customize the keybindings for the accesskeys on any website. I’d call that progress.

(Update: The latest version of my Javascript restores compatibility with Gez’s Greasemonkey script.)

Looking into the (distant) future, XHTML 2 will offer a self-documenting reformulation of accesskeys. Instead of

<a accesskey="0" href="/accessibility.html" />

XHTML 2 authors will use the self-documenting <access> element. They’ll write

<access key="0"
  title="Accessibility Statement"
  targetrole="foo:accessibility" />

followed by

<a role="foo:accessibility" href="/accessibility.html" />

The WAI offer their own set of 8 predefined roles. Other roles need to be defined in their own namespace

xmlns:foo="http://mysite.com/roles/foo"

which points to an RDF Schema defining the role(s). Alternatively, there’s a

<access key="c"
  title="Post a Comment"
  targetid="comment" />

for those instances when a custom-defined role seems like overkill.

The definition-list we’ve been talking about here is a crude stand-in for the collection of <access> elements in an XHTML 2 document. With that substitution, the same techniques for customizing keybindings will work in XHTML 2. Hopefully, that capability will be built into XHTML 2 User Agents, rather than being an afterthought, as with today’s accesskey attribute.

1. You can toggle the Accesskey menu by hitting Shift -Esc (to reclaim some screen real-estate, and avoid obscuring the bottom of the page).
2. The CSS styling is now rolled into the script, rather than loaded from Gez’s site.

For obvious reasons, if you’ve installed the previous version, you want to update. My Javascript has also been updated to detect the presence of Gez’s script and ensure that they play nicely together.

I was admiring the “doggiesaurus” dinosaur picture my 5 year old created in preschool today, as he cheerfully explained to me about their habits (they’re plant-eaters, apparently). So I turned to him and asked, “Son, when you grow up, would you like to be a scientist, who digs up dinosaur bones?” “Daddy,” he says to me, witheringly, “You mean a palæontologist.”

“Yes,” I said meekly, “a palæontologist.” “Sure.” he says, “And then, when I’m done, I can give the bones to a museum.”

Accesskeys are a very nice mechanism for making your website more accessible. You can define a set of keyboard shortcuts for common navigational tasks, making it easier for visitors, who can’t (or don’t wish to) use a mouse, to find their way around your site. For instance, on this site, hitting Alt -4 (Cntrl -4 on a Mac) takes you to the search form on the current page; Alt -1 (Cntrl -1) takes you to the main page of this blog, etc.

Unfortunately, accesskeys suffer from two big drawbacks

1. There’s no easy way for visitors to discover what accesskeys are defined on a particular site.
2. The accesskeys you define may conflict with the user’s existing keyboard shortcuts. Even if they don’t, accesskey assignments vary from site to site, so there’s no “muscle memory” advantage to them.

The first problem is easy to fix. Long ago, I put a listing of the accesskeys, defined here, in the footer of each page. Scroll down to take a look at it. The markup that generated the footer is

<div id="footer">   
<h2>Access Keys:</h2>

<dl id="AccessKeyList">
<dt>0</dt><dd><a href="/~distler/blog/accessibility.html" accesskey="0">Accessibility Statement</a></dd>
<dt>1</dt><dd>Main Page</dd>
<dt>2</dt><dd>Skip to Content</dd>
<dt>3</dt><dd>List of Posts</dd>
<dt>4</dt><dd>Search</dd>
<dt>p</dt><dd>Previous (individual/monthly archive page)</dd>
<dt>n</dt><dd>Next (individual/monthly archive page)</dd>
</dl>

<a href="/~distler/blog/archives.html" accesskey="3"></a>
</div>

and it can be included at the bottom of every page, using SSI, PHP or, in my case MovableType’s <MTInclude> directive. Of course, this definition-list didn’t have to be in the footer of the page. It could have been in a CSS drop-down menu at the top of the page or … The point is to make it unobtrusive, and yet easily-discoverable. Someone, with better design skills than I, could have found a more artful solution.

The second drawback seemed harder to surmount. Somehow, we need to let the user customize the accesskey assignments. But how?

Recently, Gez Lemon found a solution using server-side scripting. Unfortunately, it was more than a little cumbersome. As a web-author, it requires mucking with the markup of your pages¹. As a user, it involves thoroughly unnecessary back-and-forth interaction with the server. Still, it was inspirational. Once you realize it can be done, you start to think about other ways to achieve the same effect.

I wanted something that would not involve mucking with the existing markup of my pages, and which would work client-side (so as to be as fast and smooth as possible). If you’ve read this far, you probably want to see it in action. Scroll down² to the bottom of the page and hit the, hitherto mysterious, edit button. You can assign any keyboard character you want to an accesskey, though most browsers do not distinguish between uppercase and lowercase letters. If you want to disable one (or all) of the accesskeys, simply delete the corresponding character. When you’re happy, hit save. You can now use your new accesskey assignments anywhere on this blog. And they’ve been saved in a cookie, for your future surfing pleasure. If, instead, the current accesskey assignments suit you, just hit reset.

No markup was butchered to achieve this effect. All I needed to do was include this Javascript file and add initializeAccessKeys(); to the onload-handler for my pages. In fact, the Javascript uses the existing markup (a definition-list whose id="AccessKeyList")³ as an editing template for customizing the accesskeys.

I rather enjoyed crafting this, my first somewhat nontrivial bit of Javascript programming. There’s something delightfully recursive about using DOM-scripting to add event-handler attributes which, when activated, trigger other DOM-scripting operations.

I’ve only tested it in a few browsers (Mozilla, Safari and Opera), but expect it to work in others as well. Suggestions for improvements are welcome.

Postscript: Event Handlers

Getting keyboard navigation to work right in the presence of certain event-handlers seems to be a black art. All the sources I’ve looked at give incorrect advice. As a consequence, I, myself, have been doing it wrong for years now.

onclick="..."

by itself doesn’t work right. The user should be able to trigger this handler by hitting Return. But that doesn’t happen in Safari (and, perhaps, other browsers).

onclick="..."
onkeypress="..."

will cause the handler to be triggered by hitting any key. Which is not what you want: that breaks Tab-navigation. What does work is

onclick="..."
onkeypress="if(window.event.keyCode == 13){...; return false;}"

Since I haven’t seen this explained anywhere⁴, I figured I’d spell it out here, and save someone else from tearing their hair out, too.

The nonpartisan Congressional Research Service has issued their report, looking into the legality of the domestic spying program initiated 4 years ago by the President, in the wake of 9/11. Unsurprisingly, their conclusion is that it violated the Foreign Intelligence Surveillance Act and they, quietly but thoroughly, demolishes the Administration’s argument that the Sept. 2001 Authorization for Use of Military Force authorized the Administration to circumvent FISA¹ at their pleasure.

Anyone with even a vestigial interest in the Rule-of-Law in this country ought to read it. It’s heavily laden with footnotes, but if you skip those, not too difficult to make your way through.

Administration loyalists have, predictably, decried the New York Times for compromising National Security with this revelation². As Glen Greenwalt convincingly demonstrates, they don’t know what they’re talking about. (He’s been doing some excellent blogging on the NSA spying scandal.)

There’s no getting around the fact that the Adminstration has flagrantly, unrepentantly violated the Law of the land, and vows to continue to do so. They’ve had 4 years to propose changes to FISA (beyond those of the USA Patriot Act), if they felt there was an argument (which would pass Constitutional muster) for doing so. Instead, they decided to simply ignore FISA. Evidently, the Rule-of-Law is not on their radar screen. Everyone wants the President to have the tools necessary to fight the War on Terror. No one but a partisan hack would conclude that shredding the Constitution is the way to provide those tools.

So, where does that leave us? The current Majority in the Senate is, alas, of the opinion that Impeachment is a partisan club, to be wielded against one’s political opponents, rather than a solemn tool to ensure that the Executive adheres to the Rule-of-Law. Without tremendous public pressure, we’re unlikely to see substantive hearings, let alone Articles of Impeachment.

Perhaps a bumper sticker campaign is in order

WHO DO YOU HAVE TO BLOW TO GET A PRESIDENT IMPEACHED AROUND HERE?!

KING GEORGE? DIDN’T WE FIGHT A REVOLUTION ABOUT THAT?

I’m, normally, not much of a football fan, but that was an amazing game. Vince Young is a God.

And besides, how often do I get to tweak my colleague, Clifford?

After writing my two previous posts on approaches to quantum gravity, various people asked me to write something about Causal Dynamical Triangulations, a lattice model that has enjoyed a certain amount of favourable ‘buzz’ recently. I’ve been procrastinating about following up on that request because, to do a halfway decent job would require at least two post, one about generalities about lattice models of quantum gravity and one specifically about CDT. Alas, I’m not that interested in the subject, so I’ve always been able to find something else I’d rather write about …

Anyway, as a bit of New Years resolve, here’s a stab at such a post which will, alas, fall far short of what’s really required.