1. Holographic Thermalization of Quark Gluon Plazma Irina Aref'eva Steklov Mathematical Institute, Moscow II Russian-Spanish Congress Particle and Nuclear Physics at all Scales and Cosmology Saint-Petersburg, October 1 - 4, 2013

2. Outlook Quark-Gluon Plasma in heavy-ions collisions Holography description of QGP in equilibrium Holography description of formation of QGP in HIC Black Holes formation in AdS Thermalization time Dethermalization and Dethermalization time Centrality dependence

3. Quark-Gluon Plasma (QGP): a new state of matter QGP is a state of matter formed from deconfined quarks, antiquarks, and gluons at high temperature nuclear matter Deconfined phase T increases, or density increases QCD: asymptotic freedom, quark confinement

4. Experiments: Heavy Ions collisions produced a medium There are strong experimental evidences that RHIC or LHC have created some medium which behaves collectively: modification of particle spectra (compared to p+p) jet quenching high p_T-suppression of hadrons elliptic flow suppression of quarkonium production Study of this medium is also related with study of Early Universe

5. QGP as a strongly coupled fluid Conclusion from the RHIC and LHC experiments: appearance of QGP, not a weakly coupled gas of quarks and gluons, but a strongly coupled fluid. This makes perturbative methods inapplicable The lattice formulation of QCD does not work, since we have to study real-time phenomena. This has provided a motivation to try to understand the dynamics of QGP through the gauge/string duality

6. Dual description of QGP as a part of Gauge/string duality There is not yet exist a gravity dual construction for QCD. Differences between N = 4 SYM and QCD are less significant, when quarks and gluons are in the deconfined phase (because of the conformal symmetry at the quantum level N = 4 SYM theory does not exhibit confinement.) Lattice calculations show that QCD exhibits a quasi-conformal behavior at temperatures T >300 MeV and the equation of state can be approximated by e = 3 p (a traceless conformal energy-momentum tensor). Motivated to use the AdS/CFT correspondence as a tool to get non-perturbative dynamics of QGP. There is the considerable success in description of the static QGP. Review: Solana, Liu, Mateos, Rajagopal, Wiedemann, 1101.0618

7. “Holographic description of quark-gluon plasma” Holographic description of quark-gluon plasma in equilibrium Holography description of quark-gluon plasma formation in heavy-ions collisions

8. Holography for thermal states TQFT in M D -spacetime Black hole in AdS D+1 -space-time = Hologhraphic description of Quark Gluon Plasma (QGP in equilibruum) TQFT = QFT with temperature

9. Correlators with T=0 AdS/CFT Example. D=2 t Temperatute M=BHAdS with Bose gas Vacuum correlators M=AdS x-x’=x-x’=

10. Thermalization of QFT in Minkowski D-dim space- time Black Hole formation in Anti de Sitter (D+1)-dim space-time Hologhraphic Description of Formation of QGP (Hologhraphic thermalization) Studies of BH formation in AdS D+1 Time of thermalization in HIC Multiplicity in HIC Profit:

11. Formation of BH in AdS. Deformations of AdS metric leading to BH formation Colliding gravitational shock waves Drop of a shell of matter with vanishing rest mass ("null dust"), infalling shell geometry = Vaidya metric Sudden perturbations of the metric near the boundary that propagate into the bulk Chesler, Yaffe, PRL, 2011-2013 Danielsson, Keski-Vakkuri, Kruczenski, 1999 …… Balasubramanian +9, PRL, 2011, Phys.Rev.2011 Gubser, Pufu, Yarom, Phys.Rev., 2008 (I) Gubser, Pufu, Yarom, JHEP, 2009 (II) Alvarez-Gaume, C. Gomez, Vera, Tavanfar, Vazquez-Mozo, PRL, 2009 IA, Bagrov, Guseva, Joukowskaya, E.Pozdeeva 2009, 2010,2012 JHEP Kiritsis, Taliotis, 2011 JHEP

12. Deformations of AdS metric by infalling shell d+1-dimensional infalling shell geometry is described in Poincar'e coordinates by the Vaidya metric Danielsson, Keski-Vakkuri and Kruczenski 1) 2) Danielsson, Keski-Vakkuri and Kruczenski

13. Correlators via Geodesics in AdS/CFT Vacuum correlators: M=AdSTemperatute: M=BHAdS V. Balasubramanian, S. Ross, 1999

14. Thermalization with Vadya AdS Equal-time correlators

15. Thermalization with Vadya AdS Non-Equal-time correlators Equal-time correlators

16. Evaporation vs thermalization No thermalization for large l

17. t dethermalization / t thermalization J is a turning point

18. t dethermalization /t thermalization Data:.A., I.Volovich,1211.6041

19. t dethermalization / t thermalization Data:

20. Anizotropic thermalization AdS-Lifshitz-Vaidya solutions M.Taylor,0812.0530

21. Anizotropic thermalization Anisotropy decreases thermalization time. R u*u*

22. Thermalization Time and Centricity Non-centricity Kerr-ADS-BH I.A.,A.Koshelev, A.Bagrov, JHEP 07 (2013) 170 d=3 BTZ Vaidya-Kerr-AdS

23. Kerr-ADS-BH Geometry Geodesics B 1,2 = (β 1,2 − γ 2 )(β 1,2 − γ 1 ) i

24. Geodesics which start and finish at Thermal geodesics a=0 * Turning point - V. Balasubramanian, A. Bernamonti, J. de Boer, N. Copland, B. Craps, E. Keski-Vakkuri, B. Muller and A. Schafer et al., PRL, 2011

25. Geodesics which start and finish at … no “a” dependence

26. Conclusion Formation of QGP of 4-dim QCD  Black Hole formation in AdS 5 Anisotropy decreases thermalization time. Centrality dependence of thermalization time d=3 no dependence d>3 ?