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Note:These pages make extensive use of the latest XHTML and CSS Standards. They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in Mozilla. My best suggestion (and you will thank me when surfing an ever-increasing number of sites on the web which have been crafted to use the new standards) is to upgrade to the latest version of your browser. If that's not possible, consider moving to the Standards-compliant and open-source Mozilla browser.

April 27, 2007

AdS/Neutron Stars

Quite some time ago, I wrote about an ‘AdS/CFT-inspired’ model for hadron physics. Despite its crudity, it seems to capture surprisingly well the physics of the low-lying mesons (π\pi, ρ\rho, a 1a_1).

It also provides a nice laboratory for studying physics at finite baryon density. The 5D vector field, V^=12N fTr(A L+A R) \hat{V} = \frac{1}{\sqrt{2 N_f}}Tr(A_L + A_R) couples to baryon number. Choosing boundary conditions V^ 0(z)=A+12Bz 2+… \hat{V}_0(z) = A + \tfrac{1}{2} B z^2 +\dots corresponds to working at finite chemical potential μ b=AN c \mu_b = A N_c and baryon number density n b=124π 2B n_b = \frac{1}{24\pi^2} B

Domokos and Harvey added the 5D Chern-Simons interaction S CS=N c24π 2∫(ω 5(A L)−ω 5(A R)) S_{\text{CS}} = \frac{N_c}{24\pi^2} \int (\omega_5(A_L) - \omega_5(A_R)) (where dω 5=TrF 3d\omega_5 = Tr F^3) to the model and found a remarkable effect. At finite baryon density, the 4D effective action contains a term S=∫d 4x…+μϵ ijk(ρ i a∂ ja k a+a i a∂ jρ j a)+… S = \int d^4x\, \dots +\mu\epsilon^{i j k} (\rho^a_i \partial_j a^a_k + a^a_i \partial_j \rho^a_j)+\dots (where μ∝n b\mu\propto n_b). Above some critical value of the baryon density, the addition of this term induces a translational- and rotational-invariance breaking condensate of ρ\rho and a 1a_1.

At least in this model of Erlich et al, the critical density is in the same ballpark as that of nuclear matter. So, perhaps, this condensate actually forms in neutron stars.

It would be interesting to repeat the calculation in other models, like the Sakai-Sugimoto model, and see how that affects the prediction for the critical density.

Posted by distler at 10:03 AM | Permalink | Followups (4)

April 26, 2007

Effective Field Theory and Gravity

I’ve written, before, about the fact that, at energies below the Planck scale, there’s a perfectly nice effective field theory of gravity. But what is its range of validity? The naïve answer is that it should be trustworthy when curvatures are small, and particle momenta are sub-Planckian. That’s clearly true, but are there other regimes when the effective field theory analysis is naïvely valid but, in fact, breaks down?

Arkani-Hamed et al have a proposal for such a breakdown.

Continue reading “Effective Field Theory and Gravity” ...
Posted by distler at 11:21 PM | Permalink | Post a Comment

SVG Comments

It’s been a while since I did anything really technologically innovative with this blog. But progress marches on, and it’s time to kick it up a notch. Mozilla/Firefox, Opera and the prerelease version of Safari all support inline SVG. So perhaps the time is ripe to enable SVG comments.

Continue reading “SVG Comments” ...
Posted by distler at 1:44 AM | Permalink | Followups (7)

April 13, 2007

Instiki and Atom

If you’re serving rich content (inline MathML, inline SVG, …), then RSS 2.0, with its poetic specification and undefined content-model, is a thoroughly inadequate syndication format. Atom, on the other hand, provides a solid foundation for advanced news aggregators, like Venus (which powers Planet Musings).

When I started working on my branch of Instiki, one of the main items on my TODO list was to ditch RSS 2.0 in favour of Atom syndication. I finally got around to doing that, recently.

I also ported MathML::Entities to Ruby, so that Instiki now translates named entities before sending them over the wire. This is good news for users of non-MathML-aware XHTML-UA’s, like Safari and Opera.

Well, … sorta.

Safari’s DOM support in XHTML is pretty thoroughly broken. S5 slideshows don’t work at all (and even crash some recent WebKit nightlies). Until Safari gets fixed, the only reasonable alternative is to send S5 slideshows as text/html. That means no MathML (of course) and no inline SVG for Safari.

Speaking of inline SVG, I was struck by John Baez’s recent post over at the n-Category Café. He needed to draw some Young Tableaux, and couldn’t figure out a nice, simple way to do it.

The answer, John, awaits you, when you “View Source” on this entry.

Examples of Young Tableaux

Start using inline SVG for such simple tasks and, if it works well, I’ll enable SVG in the comments, too.

Posted by distler at 7:59 PM | Permalink | Followups (12)

April 9, 2007

Decoupling N=8 Supergravity

There’s been a lot of buzz, lately, about the possibility that maximal (N−8N-8) supergravity might be a finite theory in d=4d=4. These supergravity theories arise as the low-energy limits of Type-II string theory compactified on T 10−dT^{10-d}. The question is: is there a decoupling limit, in which one can hold M (d)M_{(d)}, the Planck mass in dd dimensions, fixed, while decoupling all of the degrees of freedom except for the massless supergravity multiplet.

As I explained recently, the massless scalar fields of the supergravity multiplet take values on ℳ=E˜ n/K n\mathcal{M}=\tilde{E}_n/K_n, where n=11−dn=11-d. Type II string theory, compactified on T 10−dT^{10-d}, yields not quite that. Because of the massive charged states of the theory, the continuous E˜ n\tilde{E}_n symmetry is broken to E˜ n(ℤ)\tilde{E}_n(\mathbb{Z}), which is, in fact, a gauge symmetry, and the true moduli space is ℳ/E˜ n(ℤ)\mathcal{M}/\tilde{E}_n(\mathbb{Z}).

Might there be a decoupling limit (as one approaches the boundary of the moduli space), in which all of the massive degrees of freedom decouple, leaving only the supergravity multiplet (whose moduli space, in the limit, looks like ℳ\mathcal{M})?

Green, Ooguri and Schwarz say no (at least, for d≥4d\geq 4). The computation is fairly trivial, and I suspect that the result is well-known to most of you. For variety, let me present it in M-theory language (which has the advantage of being a bit more concise).

Continue reading “Decoupling N=8 Supergravity” ...
Posted by distler at 1:49 AM | Permalink | Followups (17)

April 8, 2007

10.4.9

For the most part, Macs “just work.” And one tends to forget, after a while, that one is supposed to be circumspect and cautious in updating one’s System software.

I was reminded, briefly, of how the other half lives by the MacOSX 10.4.9 update. I installed it via “Software Update…” and, afterwards, a variety of glitches appeared.

  • The keyboard volume controls no longer functioned.

  • Mounting Disk Images no longer worked, either by double-clicking on the .dmg or at the commandline. Typing

     % hdiutil mount foo.dmg

    yielded the rather ominous

     load_hdi: timed out waiting for driver to load
 load_hdi: timed out waiting for driver to load
 ...

Dang! This meant that it would not even help to download the Combo updater, and try doing the update again (an oft-recommended cure for random ailments).

Instead, I deleted

  /System/Library/Extensions.kextcache
  /System/Library/Caches/com.apple.kernelcaches/

crossed my fingers, and rebooted. Everything worked!

Posted by distler at 11:24 PM | Permalink | Followups (1)

April 4, 2007

Sacrificial

the cat

When he seeth the blood upon the lintel and on the two side posts, the Lord will pass over the door and will not suffer the destroyer to come in unto your houses to smite you.

Ah!

So that explains the bloody mockingbird carcass that the cat dragged across the front porch (and then loudly scratched at the door to inform us about) during the Passover Seder.

She was trying to protect us.

Posted by distler at 11:02 PM | Permalink | Followups (1)