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June 25, 2007

Strings 2007, Part 1

Well, the idea of live-blogging Strings 2007 kinda evaporated with the flaky wireless in the lecture hall (keeps going down every few minutes), and the fact that the place is just packed (there are over 450 participants, and the room seems to be standing room only). I guess it’s all for the best; I think I’m better when I write in complete sentences.

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{10}^{32}/cm2^2s are scheduled for the end of 2008. No word on when they will reach the design luminosity of 10 34{10}^{34}/cm2^2s.

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{10}^{29}, will collect millions of minimum bias events and measure the di-jet cross section.
  • With 100 pb1^{-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{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 𝒩=4\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 tree)=div+f(λ)(log(s/t)) 2 \log(A/A_{\text{tree}}) = \text{div} +f(\lambda) (\log(s/t))^2 where div = jiS div(s j,j+1) iS div(s) =12ϵ 2F(λ(s) ϵ/2μ ϵ)+12ϵG(λ(s) ϵ/2μ ϵ) \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 (λddλ) 2F(λ) =f(λ) (λddλ)G(λ) =g(λ) \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+ϵd=4+\epsilon dimensions. f(λ)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/N1/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 Ae λ2π(Area) cl 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 DpDp brane for p=3+ϵp=3+\epsilon, where the spacetime metric is ds 2=f 1/2dx 4+ϵ 2+f 1/2(dr 2+r 2dΩ 5ϵ 2) {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)=c pg p 2Nr 4ϵ,g p 2=g 2μ ϵ(4πe γ) ϵ/2,c p=2 2ϵπ 3ϵ/2Γ(2ϵ/2) 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(λ)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=4N=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×S 2AdS_2\times S^2; instead, the S 2S^2 is replaced by a geometry with only an SO(2)SO(2) (instead of SO(3)SO(3)) symmetry, and the attractor values of the scalars in the vector multiplet become functions of the polar angle, ϕ attr=ϕ(θ)\phi_{\text{attr}}=\phi(\theta). So V effV_{\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 …

Posted by distler at June 25, 2007 10:30 AM

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6 Comments & 3 Trackbacks

Re: Strings 2007, Part 1

Jacques,

thanks for your reporting. Could you do us stay-at-home-rs a favour and urge the organisers (and yes I know they have to do a million things) to get the video and slides online? We are waiting to start the “String cinema” here in Munich!

Posted by: Robert on June 25, 2007 11:07 AM | Permalink | Reply to this

Re: Strings 2007, Part 1

Dear Robert!

patience please, we are working hard here!
the most heavily requested talk so far
is already on the net!!

(we leave it for you guys out there and at home to guess which one it is ;-)

-karl

Posted by: karl on June 26, 2007 7:49 AM | Permalink | Reply to this

Re: Strings 2007, Part 1

Karl,

I know you probably now have a million other things to do, but would it be possible to indicate on the web page which links (slides/video) actually lead to data?

Furthermore, your streaming server seems to be a bit too slow. Could you perhaps also provide links to download full talks (at a slower rate) to replay them as a whole?

Posted by: Robert on June 26, 2007 10:25 AM | Permalink | Reply to this

Re: Strings 2007, Part 1

Well, for slides at least, URL truncation is your friend. Doesn’t seem like there’s any such trick for video as best I can tell.

Posted by: Aaron Bergman on June 26, 2007 10:43 AM | Permalink | Reply to this

Re: Strings 2007, Part 1

Karl:

The videos seem to be working for me (USA, west coast). Are you handling the multimedia for Strings’ ‘07 (videos + .PDFs)?

I need to contact the program chair (name + email) to get permission to do some multimedia tests (iPod/iTunes) with these videos. Can’t find it on the Strings ‘07 website, just the webmaster emails. Help? (I went to the IFT sponsor site, but the Miembros section has a generic list of staff.)

Posted by: joe on June 27, 2007 3:52 PM | Permalink | Reply to this

Re: Strings 2007, Part 1

While you’re here, would you mind converting the .ppt and .jnt files to pdf for those of us who aren’t Microsoft enabled?

Thanx

Posted by: Aaron Bergman on June 28, 2007 2:42 PM | Permalink | Reply to this
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Weblog: Asymptotia
Excerpt: I’ve just noticed that Jacques Distler will be blogging from Strings 2007 (his first post is here). Excellent! I hope that others will be too. If you learn of anyone else who will be blogging from the conference (either physics content or other a...
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