Musings

Well, my iBook returned safely¹, with a brand new logic board and brand new hard drive. Recovering the data from the old drive proved to be a more harrowing experience than I could have imagined. CarbonCopyCloner and the underlying commandline utility, ditto, seem to react very badly to certain types of disk errors: freezing up when they encounter some damaged files, silently skipping over others. I think I’ve got everything back in place now, but it took several days of effort (and a good semi-recent backup).

Anyway, Luboš points to a recent note by Vafa, in which Cumrun makes the obvious point that “most” low-energy effective field theories coupled to (super)gravity do not have UV completions. Despite making apparent sense at low energies, they are, in fact, inconsistent. As I’ve been trying to emphasize in recent posts, this is bound to be true, whether you think the short distance behaviour is governed by a UV fixed point or by String Theory.

It’s already true in 10 dimensions. If we demand the cancellation of gauge and gravitational anomalies (an IR phenomenon), there are precisely 4 consistent low-energy theories coupled to 10-dimensional $N=1$ supergravity

1. $SO(32)$
2. $E_8\times E_8$
3. $E_8\times U(1)^{248}$
4. $U(1)^{496}$

But only the first two have UV completions as String Theories. If it’s true in 10 dimensions, it’s surely true after compactification as well, and Cumrun brings up a bunch of examples of generic classes of low-energy theories which do not seem to arise as compactifications of String Theory.

This is interesting. But, ultimately, what will be more interesting is to show not gross features distinguishing “bad” low-energy effective field theories from the “good” (i.e., embeddable in String Theory) ones, but fine features. For instance, nothing about the consistency of low-energy physics (or any anthropic reasoning) requires 3 generations. We could, just as well, get by with 2 or 1. But those 4-d effective field theories don’t seem to be realizable in String Theory².

Despite the enthusiastic belief that ‘anything’ is realizable somewhere on the Landscape, I’m gonna wager that is far, far, from true. And, in figuring out what’s actually possible, we will learn much.

Update (10/6/2005): A 1-Generation Model

In the comments, Volker Braun mentions that it might be possible to construct a 1-generation model as a variant of a heterotic compactification recently considered by him and collaborations at Penn. At least, at the level of crudity that I was making the conjecture, that turns out to be the case.

The Calabi Yau manifold, $X$, that they consider has fundamental group $\mathbb{Z}_3\times\mathbb{Z}_3$, and its universal cover, $\tilde{X}$ is a fiber product of two $dP_9$s. That is, $\tilde{X}$ is elliptically-fibered over a base which is, itself, an elliptically-fibered del Pezzo surface ($\mathbb{P}^2$ blown up at 9 points). In their paper from last October, they work out the geometry of $\tilde{X}$, and show that, with the right sort of fibration structure (three $I_1$ singularities and three $I_3$ singularities), one can find a family of $\tilde{X}$s with a freely-acting $\mathbb{Z}_3\times\mathbb{Z}_3$. The hodge numbers of $\tilde{X}$ are $h^{1,1}(\tilde{X})=h^{2,1}(\tilde{X})=19$ and so $X$ has $h^{1,1}(X)=h^{2,1}(X)=3$.

Equivariant bundles on $\tilde{X}$ descend to bundles on $X$, and in their followup paper from this May, they describe how to construct suitable equivariant bundles on $\tilde{X}$ to build a 3-generation $SO(10)$ model on $X$ (together with suitable doublet-triplet splitting, etc.). To get the rank-4 bundle, $V$, to embed in the visible $E_8$, they follow a 2-step procedure. First construct a rank-2 bundle, $W$ on the base as an extension $$0 \to L^{-1} \to W \to L\otimes \mathcal{I} \to 0$$ and then, after pulling back to $\tilde{X}$, construct another extension $$0\to \mathcal{L}\oplus\mathcal{L} \to V \to \mathcal{L}^{-1}\otimes \pi^*W\to 0$$ Here $L$ is a certain line bundle on the base, $\mathcal{L}$ is a line bundle on $\tilde{X}$, and $\mathcal{I}$ is an ideal sheaf of a set of points, $\{p_i\}$. I’ve brutally suppressed the equivariant structures on all the bundles involved.

Anyway, to get a 3-generation model, they choose $L= \mathcal{O}(2f)$, where $f$ is the divisor class of a generic fiber on $dP_9$ and $\{p_i\}$ is a generic set of 9 points permuted by the $\mathbb{Z}_3\times\mathbb{Z}_3$ action. To get a 1-generation model, Volker says, choose $L= \mathcal{O}(f)$ and $\{p_i\}$ a set of 3 points, the locations on the base of the $I_3$ fibers of $\tilde{X}\to B$. (Note that $\mathbb{Z}_3\times\mathbb{Z}_3$ does not act freely on the base. So, rather trickily, we obtain a rank-4 bundle, $V$, whose index is 1/3 that of the previous case, which yielded 3 generations.)

So, it seems, there is already a counterexample to my conjecture about 1-generation models. But it did give me an excuse to mention this very beautiful construction by the Penn group, so it’s not a total loss.

William Morgan has released a Ruby port of itex2MML.

To celebrate, I’m releasing another minor update to itex2MML. In the new version:

1. Fixed a compilation problem with flex 2.5.31.
2. Added a “unary plus” to match “unary minus”, and improved the invocation of unary plus/minus (thanks, William)
3. Fixed stretchy delimiters. “\left(” is stretchy. “(” is not stretchy. Similarly for other delimiters and their corresponding right delimiters. Left and right stretchy delimiters must be matched (as in TeX). As in TeX, \left( will match \right] and you can use the null delimiter (\left. and \right.).

I was never really happy with the way stretchy delimiters worked in itex2MML until now.

Anyway, itex2MML 1.02 contains MacOSX and Linux binaries, as well as the source to compile your own.

Apologies for the light blogging. My iBook (from which I do my blogging) developed a problem with the ATA Controller chip last week, and had to be sent out for repair. It is currently sitting in the Apple Repair facility in Houston, awaiting Rita… repair.

The other reason I haven’t been posting much is that I’ve had this post in preparation, and I’ve had trouble psyching myself up to post it.

In a previous post, I outlined the tough row that anyone hoping to construct a theory of quantum gravity needs to hoe. One of the possibilities I discussed is that the UV behaviour of quantum gravity might be controlled by a UV fixed point. There was an interesting discussion, in the midst of which, the work of Reuter and collaborators was mentioned. My response was a bit cursory. It’s a big body of work, and responding properly would really require a full-length post.

itex2MML is the engine we use to convert TeX input to MathML output. It’s used by my plugins for MovableType, WordPress and ecto. Originally written by Paul Gartside, I’ve sorta been its default maintainer these past several years.

So you can imagine that I was pleased to learn that the forthcoming AbiWord 2.4 uses itex2MML and gtkMathView to generate and display MathML.

Francis James Franklin and Marc Maurer put a lot of effort into adapting itex2MML for use in AbiWord and, at the same time, cleaning up the code considerably.

I’ve decided to fold their changes into my distribution and bump the version number up to 1.0.

One of the nifty new features of itex2MML 1.0 is the improved error-reporting. Unfortunately, Mozilla, for some reason, decides to “hide” <merror> elements in display equations. So, to see the new, improved error messages, you need to add

merror {display:inline;font-size:1em;}

to your CSS stylesheet.

I’ve also decided to start distributing both Linux and MacOSX binaries, in addition to the source code. Let me know if you have trouble with the binaries or in compiling the source code from scratch.

Whither Safari?

Back in June, I wrote excitedly about the new open-source WebKit, and how it might soon lead to MathML support in Safari. The MathML in Webkit project doesn’t seem to have gone anywhere (though there’s been a flurry of activity on SVG support).

In the meantime, Frank, who’s the maintainer of the MacOSX port of AbiWord, helped Luca Padovani port gtkMathView to MacOSX. So there’s a whole new, high quality, MathML rendering engine on MacOSX¹. And it’s highly modular, supporting a variety of frontend inputs and backend renderers.

Is someone interested in working with Luca to incorporate gtkMathView as Safari’s MathML rendering engine?

Update (9/15/2005):

A minor revision, itex2MML 1.01, solves the problem noted by Gong yi Liao below. Subscripts and superscripts for \det, \gcd, \inf, \lim, \liminf, \limsup, \max, \min, \Pr and \sup are now handled correctly² in display equations.

If you have compilation problems, please give some details as to the system you’re compiling on.

After long discussions, the Physics Advisory Committee for the arXivs has recommended a reorganization of the physics archives. It’s a fairly drastic overhaul, and you can read about the proposed new categories.

Among the biggest changes:

• astro-ph has been broken into four categories, based roughly on distance-scale
  • physics.AC: Cosmology
  • physics.AG: Galaxies
  • physics.AS: Stars
  • physics.EP: Earth & Planetary
• The cond-mat categories have been thoroughly reorganized.
• hep-ph has been split into
  • physics.HP: General Phenomenology
  • physics.HQ: QCD
• “Supercategories” have been introduced.
  • Subscribing to physics.SS gets you all of condensed matter and AMO.
  • Subscribing to physics.AA gets you all the astrophysics categories.
  • Subscribing to physics.HH gets you all four high energy physics categories.
  • Subscribing to physics.NN gets you all of nuclear physics.

The form of paper IDs will change to match the new categories. And, yeah, there are a lot more moderators than there were previously.

Your comments on these changes are being solicited, so please look over the changes and offer whatever feedback you feel is needed.

The Chronicle of Higher Education has published a short piece (subscribers only) on the addition of Trackback support at the arXivs.

Compared with scholars in other academic fields, physicists have a reputation for forging ahead in the digital landscape. The World Wide Web came out of a particle-physics lab, and physicists pioneered the concept of making scientific papers freely available to all. For more than a decade, physicists have been posting their manuscripts on a public database, known as ArXiv (http://www.arxiv.org), even before they submit the work to journals for publication. Now the same preprint site, hosted by the Cornell University Library, is taking another leap forward: creating an archived comment system to accompany the papers.

And yes, they did quote yours truly:

In theory the process will promote a more free-flowing exchange of ideas among scientists. In the past, physicists would react to papers by talking in hallways or writing formal responses. The new process allows them to offer “quicker feedback that wouldn’t necessarily otherwise propagate very widely,” says Jacques J. Distler, a professor of physics at the University of Texas at Austin. He has lobbied for such a system for years in conversations with Paul Ginsparg, a professor of physics at Cornell who started ArXiv in 1991 and now serves as an adviser. Mr. Ginsparg asked the library staff at Cornell to enable TrackBacks, which they did late last month.

In related news, various non-blog sites like John Baez’s This Week’s Finds and CosmoCoffee have become Trackback-enabled¹.

For several hours, this evening, the previous entry was truncated, mangled, ill-formed poo. Both the itexToMML plugin for MovableType, and the corresponding plugins for ecto were misbehaving.

They were both written to use Perl’s bidirectional pipes (IPC::Open2) to filter the posts through itex2MML.

my $pid = open2(*Reader,*Writer, "itex2MML -");
print Writer $_";
close Writer;
my @out = <Reader>;
waitpid $pid, 0;
my $html = join('',@out);

For some reason, none of my hundreds of previous posts ever triggered this bug. Nor, indeed, had the, slightly shorter, original version of that post. Urs had reported problems with some of his posts, but I could never track down the problem. But here was a real-live instance, where merely adding a paragraph of text caused both ecto and MovableType to act up.

So, there I was, tearing my hair out in frustration, until I finally decided to rewrite these plugins to use temporary files instead of bidirectional pipes. Maybe a little less elegant and efficient, but a lot more stable.

If you use ecto as a blogging tool, you definitely want the new version of the itexToMML text filter plugins. If you are running MovableType on MacOSX (and possibly other operating systems), you may want the new version of the MovableType plugin as well.

Today was the first class of the new semester. And this year, again, is my turn to teach String Theory. This year I decided to give a slightly extended version of my usual introductory lecture, explaining why one might want to study quantum gravity and, if so, why String Theory is the only plausible vehicle for studying it.

The arguments are old, but it occurred to me recently, that they are not as ubiquitously understood as they might be. So, as a public service, I decided to post a précis here.