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March 26, 2008
Bagger-Lambert
The low-energy theory on a (stack of) D2-brane(s) is a maximally-supersymmetric gauge theory in 2+1 dimensions. The Yang-Mill multiplet has a gauge field and 7 real scalars in the adjoint representation. At least if you are out on the Coulomb branch, where the gauge symmetry is Higgsed down to the Cartan, you can dualize the gauge fields to another scalar, which is circle-valued.
The M2-brane is obtained as the strong-coupling limit of this theory. The radius of the circles (one for each element of the Cartan subalgebra) go to infinity, and the R-symmetry is promoted to . This strong-coupling limit is superconformal, but the above description is effective only for the free theory, where the M2-branes are separated (away from the origin, the moduli space looks like ). The theory of coincident M2-branes is an interacting SCFT which, so far, does not have a Lagrangian description. But there’s no theorem that rules out a Lagrangian description, so there may just be one.
Bagger and Lambert recently proposed a very interesting maximally supersymmetric interacting 2+1D Lagrangian field theory which, at least classically, seems to be superconformal. It does not arise as the dimensional reduction of some higher dimensional theory, and so it was missed in previous attempts at tackling this problem.
I never got around to blogging about Bagger and Lambert’s paper, but Bandres, Lipstein and Schwarz wrote a nice followup, which gives me an excuse to return to the subject.
Update:
Whoops! Even as was typing this, Mark van Raamsdonk came out with a paper making some of the points below. I’d better hurry up and post this, before there are yet-more followup papers to discuss.March 21, 2008
Google Summer of Code
Are you a (graduate or undergraduate) student with some free time this summer? Wanna earn $4500 doing a great public service? Google Summer of Code will pay you a stipend to work on WebKit. Among the project ideas listed, the one most relevant to readers of this blog is the project to bring MathML support to WebKit.
If you’ve tried reading this blog in Safari, or on an iPhone, you know how great that would be.
Just don’t let someone cajole you into settling for a stylesheet.
March 16, 2008
Fiscally Conservative
No doubt, as this political season progresses, we will hear all sorts of dire warnings about the terrible things that will happen to the Economy, if a Democrat is elected to the Presidency. Surely, he (and, yes, it will be a he) will follow in the footsteps of his predecessors, raise taxes, boost spending, and drive the Economy into the ground. If you want good stewardship of the Economy, vote for the Republican, as they are — after all – the party of business.
Back in 2000, in my pre-blog era, I decided to compile a few statistics to test out these assertions. Now that 2008 has rolled around, I’ve updated my spreadsheet to include the George W Bush era, and answer a few of the objections to the previous, not-widely-circulated, version.
I decided to look at two items: budget deficits and real GDP growth. The historical data goes back to 1930. And I did the simplest possible thing: separate out the time-series into Republican and Democratic Administrations, computing the average annual budget deficit, and the average annual real GDP growth for each.
Now, there are several immediate objections you could raise.
- There are, to be sure, lots of exogenous factors which influence economic performance. In any given year, one can ascribe performance to something other than who occupies the White House. But that’s where the law of large number comes into play. If you average over many years, these exogenous factors should cancel out. The longer the historical baseline, the more likely it is that you’re seeing a real “inter-party” effect.
- That said, the Great Depression and World War II were truly singular events with a dramatic effect on these averages. In 1932, real GDP contracted 13%. Perhaps it’s unfair to blame the Great Depression on the Republicans. By the same token, real GDP contracted 11% in 1946, in the great post-War contraction. It would be equally unfair to blame that on the Democrats. On the deficit side, the cost of waging WWII was extraordinary. The On-Budget Deficit in 1943 was an eye-popping 30.8% of GDP. For both of these reason, you might not want to take the first two rows, in each of the tables below, too seriously.
- Less obvious, but equally salient, you probably should assign the performance during the first year of each Administration to the previous one. Arguably, the economic policies of the Administration only really begin to kick in its second year. I’ve presented the data both ways.
March 15, 2008
Phun with Rails
Content-management systems that produce well-formed XHTML are not exactly thick on the ground. When it comes to Wiki software, there’s my branch of Instiki and, … umh ….
Which means that Instiki gets more than its share of attention from those interested in the question of whether XHTML is suitable for the Web.
Philip Taylor has been tireless in poking holes in various peoples’ XHTML implementations. Recently, Philip found a pair of issues in Instiki. Both were quickly fixed, but they illustrate my general maxim that any instance of a well-formedness issue is very likely an XSS issue as well.
Of the two issues that Philip found, the more serious one had to do with the author IP Address displayed at the bottom of each wiki page, next to the author’s name. What could be dangerous about an IP Address?, you ask. Well, in this case, it’s generated using Rails’s request.remote_ip method. And that, in turn, uses the HTTP Client-Ip header, if one has been set.
Install, say, Firefox’s Modify Headers extension, and you can set the Client-Ip header to whatever the heck you want. As Philip ably demonstrated, this can make the targeted page ill-formed, but it can equally-well be used to inject an XSS attack.
Arguably, Rails itself should take care that this method returns an actual IP address, rather than arbitrary garbage, but it’s easy enough to fix at the application level.
require 'resolv'
def remote_ip ip = request.remote_ip logger.info(ip) ip.gsub!(Regexp.union(Resolv::IPv4::Regex, Resolv::IPv6::Regex), '\0') || 'bogus address' end
Anyway, the bottom line is: if you’re using my branch of Instiki, please upgrade immediately to version 0.14pre(MML+).
If you’re using the main branch of Instiki, I have committed the requisite fixes to SVN Source Tree and contacted the maintainer (twice). Presumably, he will roll out a security update.
Update (3/17/2008):
Matthias has released new version of the main branch of Instiki, with the fixes rolled in.March 10, 2008
Exceptional F-Theory.
I’ve been reading Beasley, Heckman and Vafa’s recent 125 page opus, hoping to get through it before the promised Part II comes out.
F-theory is the fancy name for Type IIB string theory with 7-branes. If we compactify on