Skip to the Main Content

Note:These pages make extensive use of the latest XHTML and CSS Standards. They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in Mozilla. My best suggestion (and you will thank me when surfing an ever-increasing number of sites on the web which have been crafted to use the new standards) is to upgrade to the latest version of your browser. If that's not possible, consider moving to the Standards-compliant and open-source Mozilla browser.

May 18, 2006


Several very interesting recent papers applying AdS/CFT techniques to study properties of the quark-gluon plasma, as seen at RHIC (see this post for some earlier applications of AdS/CFT to RHIC). I’ll talk about two here, and two in my next post.

Liu, Rajagopol and Wiedemann looked at the jet-quenching parameter, q^\hat{q}, a measure of the energy-loss of high-p Tp_T partons as they move through the quark-gluon plasma. In the so-called dipole approximation, valid for small transverse distances, LL, it is related to the expectation-value of a Wilson loop in the adjoint representation, W A(C)e q^L L 2/4 \langle W_A(C)\rangle \sim e^{-\hat{q} L^- L^2/4} where CC is a light-like rectangle, of extent L L^- in the x x^- direction and length LL in the transverse direction. Beyond the dipole approximation, they take this as the definition of q^\hat{q}: the coefficient of L L 2/4L^- L^2/4, for small LL, in the expansion of logW A(C)-\log\langle W_A(C)\rangle .

For 𝒩=4\mathcal{N}=4 SYM, in the large-NN, large λ=g 2N\lambda= g^2N limit, this expectation value can be computed using AdS/CFT in an AdS5 blackhole background and the large-NN relation, logW A(C)=2logW F(C)\log \langle W_A(C)\rangle =2 \log \langle W_F(C)\rangle. The result is q^ 𝒩=4=π 3/2Γ(3/4)2Γ(5/4)λT 3 \hat{q}_{\mathcal{N}=4}= \frac{\pi^{3/2}\Gamma(3/4)}{\sqrt{2}\Gamma(5/4)}\sqrt{\lambda} T^3

What’s measured in experiments is some time-averaged value of the jet-quenching parameter, as the plasma cools. Putting in the parameters relevant to RHIC (N=3N=3, α s1/2\alpha_s\sim 1/2), q^ 𝒩=4\hat{q}_{\mathcal{N}=4} turns out rather too small compared to the experimentally-measured value.

Alex Buchel decided to look at the same calculation in the 𝒩=1\mathcal{N}=1 supersymmetric cascading gauge theory dual to the Klebanov-Strassler background1. He found q^ KSq^ 𝒩=4=1+cM 2N eff(T)+O(M 4N eff 2(T)) \frac{\hat{q}_{\text{KS}}}{\hat{q}_{\mathcal{N}=4}}= 1+ c\frac{M^2}{N_{\text{eff}}(T)} + O\left(\frac{M^4}{N_{\text{eff}}^2(T)}\right) where N eff(E)2M 2log(E/Λ),forEλ N_{\text{eff}}(E)\sim 2 M^2 \log(E/\Lambda),\quad\text{for}\, E\gg\lambda and the constant, c1.388c\simeq -1.388. At least for TΛT\gg \Lambda, the ratio increases with increasing temperature.

The speed of sound in the plasma has, for the cascading gauge theory, has a similar expansion in powers of M 2/N eff(T)M^2/N_{\text{eff}}(T) v s 2=13+49M 2N eff(T)+O(M 4N eff 2(T)) v_s^2 = \frac{1}{3} + \frac{4}{9}\frac{M^2}{N_{\text{eff}}(T)} + O\left(\frac{M^4}{N_{\text{eff}}^2(T)}\right) Buchel conjectures2 the relation q^ KSq^ 𝒩=4=1+9c4(13v s 2) \frac{\hat{q}_{\text{KS}}}{\hat{q}_{\mathcal{N}=4}}=1 +\textstyle{\frac{9c}{4}}\left(\textstyle{\frac{1}{3}} -v_s^2\right) and proposes to apply this to QCD, by plugging in the QCD sound speed in the regime relevant to RHIC.

1 The near-horizon geometry N1N\gg1 D3-branes and MM fractional D3-branes at the tip of the conifold, which is dual to an SU(N+M)×SU(N)SU(N+M)\times SU(N) 𝒩=1\mathcal{N}=1 gauge theory, with a pair of chiral multiplets in the (N+M,N¯)(N+M,\overline{N}), a pair in the (N+M¯,N)(\overline{N+M},N), and a quartic superpotential between them. This theory undergoes a duality cascade, ending up as an SU(M)SU(M) gauge theory in the IR.

2 I would have more confidence in this conjecture if he compared more than the first nontrivial terms in each.

Posted by distler at May 18, 2006 11:45 PM

TrackBack URL for this Entry:

0 Comments & 2 Trackbacks

Read the post More AdS/QGP
Weblog: Musings
Excerpt: J/Ψ suppression at RHIC and AdS/CFT.
Tracked: August 1, 2006 11:55 AM
Read the post QGP on the Lattice
Weblog: Musings
Excerpt: Computing transport coefficients for RHIC physics on the lattice.
Tracked: December 4, 2007 12:59 AM

Post a New Comment