Musings

Rolandi on LHC

The conference kicked off with an update on the status of the LHC. Despite the March 27 accident, everything is purportedly on track for a May 2008 beam commissioning. The first collisions at 14 TeV are scheduled for July 2008. Collisions with with 156 bunches on 156 bunches at ${10}^{32}$/cm$^2$s are scheduled for the end of 2008. No word on when they will reach the design luminosity of ${10}^{34}$/cm$^2$s.

The detectors are on track. ATLAS has seen cosmic ray events in their detector.

He gave a brief overview of the physics one might hope to see.

• In the first month of running at ${10}^{29}$, will collect millions of minimum bias events and measure the di-jet cross section.
• With 100 pb$^{-1}$ (first year) will see plenty of tops (as many as Tevatron has seen to date).
• Supersymmetry: 10 events/day for gluinos or squarks lighter than 1 TeV (at luminosity of ${10}^{32}$).
• Standard Model Higgs Search: D0/CDF approaching Standard model cross section for Higgs mass near 160 GeV. Will be able to explore a range of Higgs masses before LHC turns on.

Nothing you haven’t heard before.

Maldacena on Super Yang Mills scattering at strong coupling

Juan talked about joint work with Luis Alday. They study high energy, fixed angle scattering amplitude in large-N $\mathcal{N}=4$ SYM.

Bern Dixon and Smirnov suggested an asatz for the all-orders amplitude (for MHV amplitudes, but Juan points out that, at least at strong coupling, it’s clear that the leading behaviour is independent of the gluon helicities, and hence holds for non-MHV amplitudes as well). The result is IR-divergent, but, in dimensional regularization can be written in the following form $$\log(A/A_{\text{tree}}) = \text{div} +f(\lambda) (\log(s/t))^2$$ where $$\begin{aligned} \text{div} &= \sum_j i S_{\text{div}}(s_{j,j+1})\\ i S_{\text{div}}(s) &= - \frac{1}{2\epsilon^2}F\left(\frac{\lambda (-s)^{\epsilon/2}}{\mu^\epsilon}\right) + \frac{1}{2\epsilon}G\left(\frac{\lambda (-s)^{\epsilon/2}}{\mu^\epsilon}\right) \end{aligned}$$ and $$\begin{aligned} \left(\lambda\frac{d}{d\lambda}\right)^2F(\lambda) &=f(\lambda)\\ \left(\lambda\frac{d}{d\lambda}\right) G(\lambda) &=g(\lambda) \end{aligned}$$ in $d=4+\epsilon$ dimensions. $f(\lambda)$ is called the cusp anomalous dimension. In the planar limit, the IR divergences are due to the exchange of soft gluons between adjacent hard-gluon lines.

Juan works in some “T-dual” version of AdS, corresponding to momentum space in 4-dimensions. The amplitudes, apparently, have a conformal invariance in momentum space (distinct from the real-space conformal invariance). External gluon lines with fixed (light-like) momenta correspond to light-like lines on the boundary. The string calculation amounts to finding a worldsheet, with topology of a disk, whose boundary is a polygon consisting of light-like line segments corresponding to the external gluon momenta.

Gross and Mende showed that high energy, fixed-angle scattering is dominated by a single surface at each genus. I guess, to leading order in $1/N$ (but to all order in the 't Hooft coupling), that’s the disk diagram.

At strong coupling, the amplitude is given by the area of the disk $$A \sim e^{-\frac{\sqrt{\lambda}}{2\pi} (\text{Area})_{\text{cl}}}$$ This would suffer from the same IR divergence. To cure it, Juan studies a $Dp$ brane for $p=3+\epsilon$, where the spacetime metric is $${d s}^2 = f^{-1/2} {d x}^2_{4+\epsilon} + f^{1/2} ({d r}^2 + r^2 {d\Omega}^2_{5-\epsilon})$$ and $$f(r) = \frac{ c_p g_p^2 N}{r^{4-\epsilon}}, \quad g_p^2 = g^2\mu^{-\epsilon} \left(4\pi e^{-\gamma}\right)^{\epsilon/2}, \quad c_p= 2^{-2\epsilon} \pi^{-3\epsilon/2} \Gamma(2-\epsilon/2)$$ They find the strong-coupling form of the cusp anomalous dimension, $f(\lambda)$ from the string calculation. Substituting this in, they find agreement with the BDS ansatz for the all-orders 4-point function.

There then followed a pair of talks about generalized geometry (à la Hitchin) and its applications to string compactifications. I will plead jet-lag.

Sen and Trivedi

After lunch, Ashoke Sen talked about his proof of the DVV formula for the degeneracy of 1/4 BPS states in $N=4$ supergravity (actually, for the helicity supertrace, which is a kind of index). His main conclusion is that the jumps in the spectrum, across the walls of marginal stability, can be precisely accounted for by the decay of 1/4 BPS blackholes into 2-centered 1/2 BPS “small” blackholes. It’s also possible for 1/4 BPS states to decay into pairs of 1/4 BPS states. Dunno why those don’t contribute to the index

Sandip talked about the attractor mechanism for nonsupersymmetric, extremal blackholes. He posed a very simple criterion for the existence of an attractor point. In the non-rotating case, the problem can be reduced to a finding minima of a certain effective potential, where the horizon area is equal to the value of the effective potential at the minimum. A closely related technique is Sen’s entropy function technique, which has the advantage of incorporating effects of higher derivative corrections to supergravity action, but has the disadvantage that one can only study the endpoint of the flow, rather than obtaining the full solution. In the rotating case, the near horizon geometry is no longer $AdS_2\times S^2$; instead, the $S^2$ is replaced by a geometry with only an $SO(2)$ (instead of $SO(3)$) symmetry, and the attractor values of the scalars in the vector multiplet become functions of the polar angle, $\phi_{\text{attr}}=\phi(\theta)$. So $V_{\text{eff}}$ becomes a functional this data (and a function of the charges).

Anyway, there will be several more blackhole talks later in the week. Blackhole entropy and the OSV conjecture seem to still be fertile areas of research.

More later …