## July 31, 2008

### Best Fit

Via Tommaso Dorigo, Pete Renton’s talk at ICHEP08, a report on Global Electroweak Fits and the Higgs Boson Mass. Incorporating the latest Tevatron data,

- $m_t = 172.5\pm 1.2$ GeV.
- $m_W = 80.413\pm 0.048$ GeV.
- $\alpha_s(M_Z^2) = 0.1185 \pm 0.0026$
- $m_H \lt 154$ GeV at the $95\%$ confidence level.
- $m_H = 84^{+34}_{-26}$ GeV (highly sensitive to $m_W$ and $M_t$).

## July 30, 2008

### Wall Crossing

Many of the magical result in string theory and supersymmetric gauge theories have been motivated by consideration of the spectrum of BPS states in these theories. For 16 supercharges ($\mathcal{N}=4$), this spectrum varies continuously as one moves through the moduli space. This fact is at the heart of the S-duality conjectures. For 8 supercharges ($\mathcal{N}=2$ supersymmetry), the spectrum of BPS states jumps discontinuously, as one crosses “walls of marginal stability”. As a consequence, there is usually no manifest S-duality for $\mathcal{N}=2$ theories.

Describing exactly *how* the spectrum of BPS states jumps is, however, a complicated business. and a lot of effort has gone into deriving “wall crossing formulæ.” Recently considerable progress was, apparently (I say “apparently” because the paper has not yet appeared on the arXivs), made by Kontsevich and Soibelman, who proposed a wall-crossing formula for $\mathcal{N}=2$ Seiberg-Witten Theory. Gaiotto, Moore and Neitzke provide a beautiful physical explanation for Kontsevich and Soibelman’s result.

## July 21, 2008

### T-Duality and Dual Superconformal Symmetry

One of the most interesting talks at the Simons Workshop in Stony Brook was by Nathan Berkovits, about his joint work with Maldacena. Roughly a year ago, Alday and Maldacena made a striking observation about the strong coupling behaviour of scattering amplitudes in $\mathcal{N}=4$ Super Yang-Mills at large-$N$. Namely, that they possess a conformal symmetry in *momentum space*, and can be computed using a sort of “T-dual” version of AdS/CFT. One studies Wilson loops in momentum space, which are polygons consisting of $n$ light-like edges (momentum conservation is the statement that the polygon closes). These can be computed, as the areas of a minimal surface (string worldsheet, with boundary on the polygon) in the bulk (“T-dual”) $\text{AdS}_5\times S^5$. I blogged about their work before, so I’ll refer you to my post, and the paper, for more details.

What Nathan and Juan do is provide an explanation of what T-duality is supposed to be taking place here.

## July 13, 2008

### A Clean Break

This election season has seen a lot of hand-wringing about the price of oil. McCain and Clinton had their foolish^{1} gas tax holiday proposals. More recently, Republicans have renewed calls to throw open ANWR and offshore coastal areas to drilling (at the same time as they call for a moratorium on new solar power plants, out of concern for the possible environmental impact [sic]).

None of this is going to make a whit of difference in the short term. Nor is it going to affect the long-term trend, namely that worldwide demand for oil is increasing faster than worldwide supply (the reserves in ANWR and offshore are too small to affect that picture).

Rather than get depressed, I’ve been thinking about what the Israelis are doing. Israel doesn’t have any domestic reserves to tap into. And their dependence on imported oil comes with — shall we say — a certain geopolitical cost. Instead, they’ve decided to cut to the chase and eliminate gasoline-powered vehicles. They’re going all-electric. By 2018.

## July 12, 2008

### I’m Baaaack

Sorry for the three-week hiatus; I’d decided to foreswear blogging while working on my latest paper. As a fat and lazy tenured faculty member, I can afford (and usually manage) to procrastinate about such things. But, in deference to my collaborator, a hungry postdoc without such luxuries, I decided to *focus*.

Well, mostly…