Musings

The STIX Fonts

After five years of blogging about the imminent release of the STIX fonts, they have finally been released in beta. I immediately rushed to install them. They are a huge improvement over Code2000/Code2001, which were previously required to complete the glyph coverage needed for rendering Math hereabouts.

The STIX fonts are not quite ready to replace the Mathematica/Computer Modern fonts for stretchy characters (parentheses, integral signs, etc). That will require internal changes to the Mozilla-based browsers. That, in turn, will require getting MathML working again in Mozilla Trunk. Since it’s been broken for over a year, don’t hold your breath.

arXiv API

A couple of years ago, the arXivs sprouted a Trackback interface. Now, they’ve developed an API to their search facility. Submit a query (via GET or POST), and receive the result as an Atom-formatted response.

This ties in rather nicely with one of my ambitions for Instiki: to add some bibliographic features. My plan was rather simple: store bibliographic entries in bibtex format (as retrieved from SPIRES or MathSciNet), and allow users to [cite:a_key] on their wiki pages. On the web, these would produce properly-formatted citations at the bottom of the wiki page. In the LaTeX export, it would produce \cite{a_key}, which would work with a bibtex file produced from the bibliographic database.

In such an environment, having arXiv search facilities integrated into the Instiki authoring environment would be a very nice addition¹. And this is clearly the early days of the arXiv API. I’m pretty sure that more cool things are yet to come.

For, perhaps obvious, reasons, I’ve been thinking again about sanitizing SVG. My most recent changes to the HTML5lib Sanitizer was to ensure that in constructions like

<rect width='0' height='0' fill='url(...)'/>

the referenced URL is a same-document reference, rather than one that pulls in an external resource from Lord-Knows-Where.

The white-list of elements and attributes in the HTML5lib Sanitizer is the union of a list for MathML that I came up with, and a list for SVG from Sam Ruby. I didn’t really put much thought into Sam’s list. But, once one starts thinking about things, one does start to wonder.

Is

<image xlink:href='http://bad.com/evil.svg'/>

really safe¹?

SVG is a gargantuan Specification. Even thinking about the security implications of Sam’s limited subset makes my head hurt.

As I’ve mentioned before, there is an effort afoot to enable the inclusion of MathML and SVG (and maybe other) markup in HTML5. But that’s a long way off (if it happens at all). What I really want to talk about, today, is an issue that affects us in the here and now: mixing MathML and SVG markup.

Something else happened this past week: this blog turned 5.

While I cringe, a bit, looking back at my early posts, I’m kinda gratified that I’ve managed to keep this gig going as long as I have. I’ve certainly learned a lot: about Physics, about markup and — I like to think — about what makes a useful blog post.

Back then, Physics/Math blogs were not exactly thick on the ground. In fact, the genre pretty much didn’t exist. Today, the blogroll at Planet Musings is satisfyingly long.

And yet … I’m a little dissatisfied. Many of the meatiest, most exciting, entries on that list are actually in Mathematics: our own n-Category Café, Terrence Tao’s blog, the Secret Blogging Seminar …

That make me a little jealous. Damnit! We high energy theorists were here first! I think it’s time to try to reanimate the String Coffee Table. Any volunteers?

We had Alex Maloney visiting us this week, and he gave a lovely talk about his forthcoming paper with Edward Witten on 2+1 gravity with negative cosmological constant.

You’ll recall that Witten’s proposal is that the dual CFT has a partition function of the form

where the central charge $c=24k= 3\ell/2G$, with $\ell$ the radius of AdS₃. $\chi_1(q)$ is the partition function of the famous Monster Module. For higher $k$, the first primary state above the ground state ($h=0$) has $h=k+1$. One can systematically write down the $\chi_k(q)$, but it is not known whether they, in fact, correspond to bona fide CFTs. Indeed, Gaberdiel had presented a strong (though not air-tight) argument that they cannot, for sufficiently large $k$ ($k\geq 42$).

If Gaberdiel is correct, then, either the proposal (1) is wrong, or there is no semiclassical regime for 2+1 gravity¹. In either case you can stop reading this post. If not, then an interesting question arises. Semiclassically, we expect there to be a Hawking-Page transition between hot AdS space (with inverse temperature $\beta=Im(\tau)$) and the AdS BTZ blackhole. Indeed, as a function of complex $\tau$, you expect a complicated phase structure, given by the fundamental domains for the action of $SL(2,\mathbb{Z})$.

When we Wick rotate to Euclidean time, the boundary is a torus, $\Sigma$, of modular parameter, $\tau$. Semiclassically, we expect a single bulk geometry² to dominate: a handlebody (a solid torus), $M$, whose boundary is $\Sigma$. This involves a choice of cycle, $\gamma= p\alpha +q\beta$, with $(p,q)$ coprime, such that $\gamma$ is contractible in $M$. The usual Hawking-Page transition is the flip between when spatial circle is contractible (hot AdS) and when the Euclidean time-circle is contractible (the blackhole). But, in 2+1 dimensions, the phase structure is much richer.

One thing that might puzzle you, in this regard, is how there can be a phase transition, in light of (1), where the $\chi_k(q)$ are manifestly analytic. The answer is that $\chi_k(q)$ have $k$ zeroes along the phase boundaries and, in the large-$k$ limit, these zeroes become dense, leading to the desired non-analytic behaviour.

In a phrase: Hawking-Page is Lee-Yang!

Tangentially, I think liberals should thank Fox News for indirectly providing a valuable service. It is now possible to rank the batshit-craziness of American conservatives on a single linear scale, based on when they stopped watching Fox News.

The MSSM is much-maligned for having many more parameters than the Standard Model. Of course, in the supersymmetric limit, it has no more parameters than the Standard Model. To the contrary, the Higgs quartic coupling is related to the gauge coupling, a simplification that is the source of a certain amount of trouble.

Supersymmetry breaking introduces a plethora of soft parameters. But, as we mentioned last time, we already have some quite stringent constraints on these parameters. And these have nontrivial implications for higher-energy physics.

But we’d like to do better. We’d like to extract some robust (that is to say, relatively model-independent) predictions for these soft parameters. The most promising place to look is at the gaugino masses, where Nilles and Choi have done a very nice analysis.

I’ve been planning to write some things about recent developments in string phenomenology. Unfortunately, the list of papers I want to talk about seems to grow faster than my ability to keep pace. So, rather than being as systematic as I would like, I’ll just plunge in and talk about a recent paper by Joseph Conlon. The subject is supersymmetry-breaking, and a mechanism he calls “mirror-mediation.”

First-off, I have to say that I hate the nomenclature of this sub-field, where a profusion of fanciful (and, usually, not terribly descriptive) names, of the form …-mediation, are attached to various restrictions on the form of the supergravity Lagrangian. I realize it’s hard to stop, once such a convention is established, but I think it tends to obscure more than it illuminates.

Anyway, the key problems that any of these mediation mechanisms needs to solve is to somehow avoid that the soft SUSY-breaking terms induced for the MSSM fields lead to flavour-changing neutral currents and/or large CP-violation.

Conlon points to a mechanism which might look a little ad-hoc, from the perspective of low energy effective field theory, but which is quite natural in certain classes of string vacua.

One of most useful features of my branch of Instiki is the LaTeX export. If you’ve been developing some ideas with your collaborators, and get to the point where you want to publish something, you click on the “TeX” link at the bottom of the page, and obtain a LaTeX file. Paste the contents into your favourite paper template, and ship it off to the arXivs.

Trouble is, there are some not-insignificant differences between itex and AMSLaTeX, so to make the procedure really smooth, one needs LaTeX macros to implement the various features of itex. And I’d been kinda procrastinating about writing them.

So I was overjoyed when Jason Blevins volunteered to work on this. With a few contributions from me, he managed to generate all the requisite macros (with some caveats¹). These are now incorporated in the latest version of Instiki.

I’m particularly pleased with the devilishly clever implementation of \tensor{}{} and \multiscripts{}{}{}.

But there was one issue which arose, about which I’d like to solicit the opinions of you, the users of itex2MML. There’s a conflict between the itex implementation of \binom{}{} and the one in AMSLaTeX. In AMSLaTeX, $$\binom{n}{m}$$ generates

$$\left(\genfrac{}{}{0ex}{}{n}{m}\right)$$

whereas itex (a legacy from its ancestor, webtex) produces

$$\genfrac{}{}{0ex}{}{n}{m}$$

without the parentheses.

The way I see it, there are two ways to resolve the conflict:

1. Change the behaviour of itex, to agree with that of AMSLaTeX (with which, I assume, more users are familiar). The downside is that this may break some existing pages.
2. Maintain the current behaviour, and have Instiki map \binom{n}{m} to {n \atop m} when generating the LaTeX output.

What do y’all think? Please vote in the comments.