Skip to the Main Content

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.

July 28, 2003

Leave the Country, Lose Your Songs?

I haven’t yet succumbed to the allure of the iTunes Music Store.

While nice in theory, I’ve been wondering how their DRM works in the “real world.” Sean Yeager recently posted a note to the effect that, having moved to Canada, iTunes refused to reauthorize the music he had purchased while living in the US. It appears that this was merely a glitch in the iTMS server software (compounded by misinformation from Apple Customer Support), rather than a deliberate restriction. But it’s just another reminder that you don’t really “own” the music you just purchased.

This kind of nonsense is why I held off for years from buying a DVD player. When I finally did buy one, I made sure it could be rendered Region-Free and that MacroVision could be disabled.

Posted by distler at 12:38 PM | Permalink | Followups (2)

July 27, 2003

Brad’s Epiphany

I’ve lamented before the sad spectacle that Andrew Sullivan has become in recent years. But Brad DeLong nails it: Andrew Sullivan has become Noam Chomsky.

A sorrier fate for a self-described gay Thatcherite one can hardly imagine.

Posted by distler at 3:05 AM | Permalink | Post a Comment

July 25, 2003

Not So Smart

Despite my entreaties in the past, Jon Gruber’s SmartyPants still attempts to process MathML elements (with the predictable disastrous results). The patch is so trivial, you’d think Gruber would have no objection to folding it into his distribution.

Whatever…

Posted by distler at 11:07 AM | Permalink | Post a Comment

Location, Location, Location

Here’s my office at the KITP (on a less foggy day and minus the construction, which is currently causing the building to shake).

Satellite view of KITP

Ron Donagi gave a great talk this morning about a version of Dijkgraaf-Vafa and large-N duality for compact Calabi-Yau’s. DV’s setup can be thought of as a noncompact Calabi-Yau

(1)y 2 =uv+W′(x) 2

which, generically, has n isolated A 1 singularities at u=v=y=W′(x)=0 . If W(x)=∑ i 0 n+1 a ix i, these can be smoothed by adding f μ(x)=∑ i=0 n−1 μ ix i

(2)y 2 =uv+W′(x) 2 +f μ(x)

The salient feature, according to Ron is that this degenerates to a curve (the plane {u=v=y=0 }) when the parameters a=μ=0 .

Their compact example is the intersection of a quadric and a quartic in ℂP 5 . When the quadric has rank 3, one has a genus-3 curve of A 1 singularities, while the generic quadric gives a smooth Calabi-Yau. To first order in the deformation, they compute the corresponding integrable system and solve for the open-string invariants.

It’s quite a tour de force, made all the more remarkable by the fact that it’s not clear what they are calculating. Since the Calabi-Yau is compact, the total D-brane charge must vanish. So they need to put in both N and N antibranes (on the open string side). In a supersymmetric theory, the quantity they calculate would be the related to the glueball superpotential. In this non-supersymmetric gauge theory, I’m not sure what the interpretation should be. But it’s pretty exciting if there’s something exact that you can calculate in this nonsupersymmetric theory.

Greg Moore also gave a great talk about the C-field in M-theory. Yup, it’s an element of differential cohomology, Hˇ 4 (X). Mike Hopkins gave a series of lectures last week touching on this, which went way over my head. But these guys actually have a concrete model one can wrap one’s head around.

The idea is that, up to 15-skeletons, the classifying space of E 8 bundles is an Eilenberg-MacLane space

(3)BE 8 ∼K(ℤ,4 )

So an isomorphism class of E 8 bundle on an 11-manifold is equivalent to a choice of cohomology class a∈H 4 (X,ℤ). Their concrete model for the C-field is a pair (A,c), consisting of connection on an E 8 principal bundle, P, and an honest-to-God, globally-defined, 3-form c. They can write explicit formulas for the bosonic part of the 11D supergravity action in terms of (A,c) and the field strength,

(4)G=dc+trF 2 −1 2 trR 2

which are invariant under gauge transformations

(5)(A,c)→(A+