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May 18, 2006

AdS/Au-Au

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

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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

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