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August 31, 2010
Still a Few Bugs in the System
I received the following in my email, last night (8/30/2010):
Ms. Ref. No.: XXXXXX Title: XXXXXXXXXXXXXXX Journal of Geometry and Physics Dear Professor Jacques Distler, You agreed to review Manuscript Number XXXXXX for Journal of Geometry and Physics on . Your completed review was due by 12 Oct 2010. Your review is now -42 days late. Therefore I would be grateful if you would submit you review as soon as possible at the Elsevier Editorial System at http://ees.elsevier.com/geophy/. Please login as a Reviewer using the following username and password: ...
August 30, 2010
Supertheory of Supereverything
Gogol Bordello are my current favourite band … by far.
August 9, 2010
Conservative “Physics”
Conservapedia is the brainchild of Andy Schlafly (son of conservative icon Phyllis Schlafly). It’s supposed to serve as a conservative counterweight to the notoriously liberal Wikipedia. Since, as Stephen Colbert noted, reality has a well-known liberal bias, this leads to … ahem … certain intellectual difficulties for our reality-challenged friends. Hence this article, entitled “Counterexamples to Relativity” – authored by the aforementioned Mr Schlafly himself:
The theory of relativity is a mathematical system that allows no exceptions. It is heavily promoted by liberals who like its encouragement of relativism and its tendency to mislead people in how they view the world.[1] Here is a list of 22 counterexamples: any one of them shows that the theory is incorrect.
The footnote [1] (like all the footnotes) is as hilarious as the body of the article
See, e.g., historian Paul Johnson’s book about the 20th century, and the article written by liberal law professor Laurence Tribe as allegedly assisted by Barack Obama. Virtually no one who is taught and believes relativity continues to read the Bible, a book that outsells New York Times bestsellers by a hundred-fold.
[hat tip: Talking Points Memo]
August 5, 2010
Fermions
Paper 2, of Dan Freed’s, Greg Moore’s and my series of papers on Orientifolds is out. This one focusses on the worldsheet formulation — particularly the worldsheet fermions. Because it’s for a volume dedicated to Is Singer, it’s written in a somewhat mathematical style. So, while it’s more accessible than our telegraphic Précis, it’s maybe a little tough-going for some of our physics audience. There will be some more physics-oriented papers in the series, but I don’t think any of them will be specifically devoted to the worldsheet. So, contrary to my usual practice, I’m going to try to distill some of the salient points of our current paper, here.
July 10, 2010
Redeemed
It was my housemate, Tudor Dimofte’s, first time in Aspen. So I thought I would take him up to Electric Pass. The view from the peak is, in my opinion, the most spectacular in this part of Colorado – and the ascent is a good introduction to hiking in these parts.
Unfortunately, our plans were thwarted. From the saddle, one has to traverse a very steep scree slope to reach the pass. There used to be a trail which cut, horizontally, across the scree slope and snow field (which often extended down past the trail). Unfortunately, that trail no longer exists. Instead, an indistinct trail meanders up and down the scree field, until finally petering out entirely, midway across.
Greg Moore, I later learned, had been able to reach the pass last year, but this year (he tried the day after we did), he had to turn back … as did a long line of hikers ahead of us. We tried to press on, picking our way slowly across the scree slope, but with strong gusting winds, and very unstable rock, we had to turn back a couple of hundred yards shy of the pass.
Deprived of our goal, we (and our companion, Sonia Paban) repaired to Cathedral Lake for lunch and an encounter with a very friendly marmot. Not a bad day, all in all, but a bit disappointing.
Today, however, I redeemed myself.
June 27, 2010
Crib Notes
It is difficult to get a man to understand something when his livelihood depends on him not understanding it.
— Upton Sinclair
You probably don’t want to read this post. It has an intended audience of one — my erstwhile coauthor, Skip Garibaldi.
Skip and I wrote a paper, last year, which proved that Garrett Lisi’s “Theory of Everything” (or any -based variant thereof) could not yield chiral fermions (much less 3 Standard Model generations worth of fermions). Anyone with training in high energy theory instantly apprehends the consequence that this “theory” cannot, therefore, have anything remotely to do with the real world. Unfortunately, if your PhD is in pure mathematics (or, apparently, in hydrodynamics), this may not be immediately obvious to you.
Skip has the unenviable task of lecturing on our paper at a workshop, next week, with Garrett in attendance. (Well, OK, the workshop is in lovely Banff Alberta, so perhaps some envy is warranted.) This post is designed to help him fill in the dots. It contains only material which — to someone schooled in high energy theory — is of an embarrassingly elementary nature.
You have been warned!
May 25, 2010
Third Time’s the Charm?
Rails got updated to 2.3.6, 2.3.7, and 2.3.8, within the space of 48 hours. On the theory that the “Third time’s the charm.” I decided to update Instiki for 2.3.8, this morning.
May 7, 2010
Death and Resurrection
In my last entry, I noted that Golem’s hard drive failed last Tuesday, and that the machine seemed to be ailing, with the fans constantly spinning up and down. This got steadily worse, as the week progressed, with the machine putting itself to sleep with ever-increasing frequency.
April 21, 2010
HD Failure
The hard drive on Golem went south this morning, and the machine was offline for about 14 hours. It was a fairly quick matter to procure a replacement drive from the Campus Computer Store ($60 for a 500 GB model which, since the original 250 GB drive was less than half full, should be more than adequate).
It took a couple of attempts to restore the Time Machine backup to the new drive, and considerably longer to get the machine to boot properly from the new drive. This leads me to suspect that the SATA controller may, itself, be dodgy. If so, then a fourth-generation Golem may be imminent. After 15 years, perhaps it’s time.
There was a period of a few hours between the last Time Machine backup and when hard drive gave up the ghost. Any blog comments or emails received during that period obviously didn’t make it onto the new disk. I may still be able to recover them from the old disk …
This experience (aside from killing what was otherwise shaping up to be a very productive day) left me with a new appreciation for “the cloud” and the redundancy it provides. My concerns about data security haven’t so much been allayed as supplanted.
Update (4/25/2010):
The SATA controller seems to be fine. The fans, however, are continously cycling up and down (very distracting) and the machine is afflicted by intermittent bouts of thermal runaway. I wonder if I can used wake-on-LAN over the internet, to save myself a trip into the office when that happens.March 27, 2010
Pure Spinor Signature
By some coincidence, I’ve had several discussions, recently, about Nathan Berkovits’s pure spinor formulation of the superstring. Which reminds me of something I’ve long puzzled over. Nathan invariably works in Euclidean signature, where the pure spinor constraint is
Here, , is a chiral spinor of , and is a symmetric matrix, expressing the Clebsch-Gordon coefficient, . In terms of gamma matrices,
Now, the of is a complex representation, so (1) naïvely looks like 10 complex equations in 16 complex variables. But, in reality, only 5 equations are independent, and the kernel of the pure spinor constraint is complex-dimensional (real dimension 22). In fact, it’s a complex cone over
This illuminates the above remark about the dimension of the kernel. Under the decomposition , the pure spinor constraint, (1) kills the .
The dimension (22) is crucial to getting the critical central charge correctly, in Nathan’s formulation.
Thing is, we don’t live in Euclidean signature. While, in string theory and in field theory, we are quite happy to analytically-continue in momenta, when computing scattering amplitudes, we don’t Wick-rotate the spinor algebra. That’s always done in the correct, Minkowski, signature.
It turns out that there are analogues of (1),(2) for other signatures
There’s one for each real form of . But, you’ll note, signature is notably absent. So it’s not so obvious (to me, at least) that the space of solutions to the constraint (1) has the desired dimension (22), when the signature is .
Does anyone know how to see that it does (or, alternatively, what to do if it doesn’t)?
Update (4/16/2010): Non-Reductive
I had a private email exchange with Nathan, who explained the resolution of my conundrum.
The space of solutions to the pure spinor constraint (1), for the Minkowski signature is, of course, of the form of a complex cone over . And (contra Lubos, below, who is, alas, a bit confused), is necessarily of the form , for some subgroup . However, unlike the cases in (3), is not a real form of . In fact, it’s not even a reductive group!
One can show that
where such that the decomposes, under , as
(the superscript is the weight). is the Abelian subgroup generated by the generators of , where is an vector index. Under , transforms as
The pure spinor constraint kills the , and indeed has the desired dimension.
I find this answer very striking, in how it differs from the cases in (3), In particular, it ought to have some rather important implications for the construction of amplitudes. Berkovits and Nekrasov develop a rather elaborate construction, involving Čech cohomology classes on the space . Presumably, things change significantly, when dealing with .
March 3, 2010
Coupling to Supergravity
There seems to be a certain amount of confusion about the claims of Seiberg and Komargodski in their latest paper. I have to say that I was confused, and there’s at least one recent paper arguing (more-or-less correctly) against claims that I don’t think they’re making.
So here’s my attempt to clear things up.
Consider an supersymmmetric nonlinear -model in , ie a Wess-Zumino model with target space, , a Kähler maninfold of complex dimension, . When can one couple such a theory to supergravity? A naïve reading of their paper might lead one to think that the possibilities are
- One can couple the theory to minimal supergravity if and only if the Kähler form, , on , is exact.
- One can couple the theory to “new minimal” supergravity if and only if the theory has an exact symmetry. In this case, could be cohomologically nontrivial.
- If is cohomologically nontrivial, and the theory does not have a symmetry, then the only possibility is to couple to non-minimal “16|16” supergravity.
One might think that, but one would be wrong. As Bagger and Witten showed, nearly 30 years ago, coupling to minimal supergravity does not require the Kähler form to be exact. Rather, must be an even integral class.
February 12, 2010
WYSIWYG SVG Editing In Instiki
In my quest to make Instiki the best damned piece of Math/Physics Wiki software in existence, I have been somewhat frustrated by the fact that while creating equations is easy (thanks to itex2MML), creating diagrams has not been. Yes, you can include SVG graphics, and mix equations and SVG in all kinds of interesting ways. But creating the SVG graphics required either an external GUI editor, like Adobe Illustrator or Inkscape, or manipulating the raw SVG commands manually (and, depending on the external GUI editor, sometimes both).
Well now, thanks to the great work by Jeff Schiller, Alexis Deveria and their collaborators on the SVG-Edit project, you can create, edit and manipulate inline SVG and mixed MathML/SVG content, right in Instiki.
December 31, 2009
Haiku
As part of his science fair project, my 3rd-grader needed a large number of random strings of 8 digits, in each of which “1” appears four times, and “2”–“5” appear once each.
December 28, 2009
Instiki 0.18
I just released Instiki 0.18.
It’s been half a year, since I announced the release of 0.17 and there’s lots of new stuff. So I guess it’s time for an upgrade …
New feature include:
- Syntax colouring for code blocks: ‘
html’, ‘xml’, ‘ruby’, ‘ansic’, ‘javascript’, ‘sqlite’, ‘yaml’ and ‘css’ modes. - Source view [suggested by Andrew Stacey]
- Auto-resizing Textareas scale to fit viewing area.
- Passenger support (including X-Sendfile support, if the Apache
mod_xsendfilemodule is installed). - Upgraded to Rails 2.3.5 and Rack 1.1.
- Now runs on Ruby 1.9. (If you’re a Passenger user, you may need to upgrade to Passenger 2.2.8, which works around some bugs in Ruby 1.9.1.)
- Upgraded for itex2MML 1.3.19 (which works under Ruby 1.9, and has several new features, relative to 1.3.15).
and a boatload of bugfixes.
Update (1/7/2010):
Because of some character encoding issues under Ruby 1.9 (mostly affecting My SQL users), I decided to issue a quick update to Instiki 0.18.1. [Thanks to Andrew Stacey for running these issues down.] I also added some new features: (Markdown-Extra-style) fenced code-blocks and ‘fortran’ syntax colouring. [Both courtesy of Jason Blevins.]Please
rake upgrade_instiki
before running the new version.
December 21, 2009
GraviGUT
One of the disadvantages of having waded into the Lisi affair is that I keep getting asked about related ill-conceived ideas for “theories of everything.” For the most-part, such ideas don’t have a relentless publicity machine behind them. Nor do they receive what can only be described as a credulous reception in certain corners of the Mathematics community. But still, it is assumed that one has an opinion about them.
One such idea is the “GraviGUT” of Nesti and Percacci. The bosonic fields consist of a connection for a noncompact gauge group, and a 1-form, , transforming in the 14-dimensional vector representation. More formally, we assume that is a principal bundle, and a vector bundle, associated associated to via the 14-dimensional vector representation. The fields consist of a connection on , and a 1-form, , with values in sections of .