In-medium quark potential from AdS/CFT

1. In-medium quark potential from AdS/CFT Liu HuiDept. of Phys., Jinan University collaborated with Hou De-fu, Li Jia-rong & Ren Hai-cang

2. Strong coupling at HIC STAR collaboration, PRL95(2005)122301 sQGP! NPA757(2005)184 Nucl.Phys.Proc.Suppl. 94 (2001) 19 Liu Hui: In-medium potential from AdS/CFT

3. In-medium static potential Examples Coulomb potential (vacuum, non-relativistic) Debye potential (in-medium) F: longitudinal component of polarization tensor Screening length &Effective radius 2010-10-20 Liu Hui: In-medium potential from AdS/CFT Liu Hui: In-medium potential from AdS/CFT 3

4. AdS/CFT • AdS/CFT duality relates the N=4 SYM at large Nc and ‘t Hooft coupling • Maldacena conjecture: • symmetry analog: type IIB string theory in the bulk of AdS5XS5 with the isometry group of AdS5 corresponds to the conformal group in 4D, and the isometry group of S5 to the R-symmetry group of the N=4 SYM is the uniques QFT in 4D that preserve the conformal symmetry at the quantum level. strong coupling field theory weak coupling classical supergravity Liu Hui: In-medium potential from AdS/CFT

5. Supergravity action with R-photon gauge field R is the scalar curvature • Equation of Motion Maxwell equation Liu Hui: In-medium potential from AdS/CFT

6. Correlation function from AdS/CFT • Solving the Maxwell equation and the linearized Einstein equation subject to the boundary conditions • The coefficients , give rise to the R-photon polarization tensor Policastro, Son & Starinets, JHEP0209(02)043 Liu Hui: In-medium potential from AdS/CFT

7. WKB approximation • For large and imaginary q, i.e. q = iκ≫ iT, WKB gives • The in-medium static potential Periodic function JHEP 1007:042,2010 Infinite number of poles along the imaginary axis on the complex q-plane ! Liu Hui: In-medium potential from AdS/CFT

8. Debye mass • Strong coupling (AdS/CFT) • Expand the solutions as series of u at u->0 UV divergence from non-zero temperature, removed by renormalization • The first pole contributes to Debye mass which is F(q) at q->0 Liu Hui: In-medium potential from AdS/CFT

9. Weak coupling (perturbative theory) A qualitative change in the nature of the singularities along the imaginary axis: The branch cut in the weak coupling evolves to a set of simple poles in the strong coupling! strong coupling Weak coupling Liu Hui: In-medium potential from AdS/CFT

10. Debye mass at weak coupling • Comparison Liu Hui: In-medium potential from AdS/CFT

11. Conclusion and outlook • We studied the in-medium quark potential in both strongly-coupled and weakly coupled regions within the framework of AdS/CFT correspondence. • A qualitative change of polarization tensor in the nature of the singularities has been found, which says the branch cut along the imaginary axis in the weak coupling evolves to a set of simple poles in the strong coupling. • In comparison, we found • The quantitative modification of in-medium potential may have effect on the EOS, the sound velocity, the jet energy loss, the wake potential and viscosity et al. Liu Hui: In-medium potential from AdS/CFT

12. Thank you for your attention!

13. Back up Poles exist nowhere but the imaginary axis Poles are determined by A0(0|q)=0. Taking the imaginary part of the product of A*0(u|q) and the EoM, integrating u from 0 to 1 yield If there were a complex q2 The EoM implies that the solution A0(u|q) is a convex(concave) function of u if A0(u|q) > 0(< 0). Therefore A0(u|q) could be zero only once. We already have A0(1|q) = 0 , then there is no possibility to have A0(0|q) = 0. The only location for the roots of A0(0|q) is the imaginary q-axis. trivial 2010-10-20 Liu Hui: In-medium potential from AdS/CFT Liu Hui: In-medium potential from AdS/CFT 13

14. Liu Hui: In-medium potential from AdS/CFT