Holographic Thermalization of Quark Gluon Plazma

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 Dethermalizationtime • 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 QCD: asymptotic freedom, quark confinement T increases, or density increases

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 MD-spacetime Hologhraphic description of Quark GluonPlasma (QGP in equilibruum) Black hole in AdSD+1-space-time = TQFT = QFT with temperature

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

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

11. Formation of BH in AdS. Deformations of AdS metric leading to BH formation • Colliding gravitational shockwaves • 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 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 Danielsson, Keski-Vakkuri , Kruczenski, 1999 …… Balasubramanian +9, PRL, 2011, Phys.Rev.2011 Chesler, Yaffe, PRL, 2011-2013

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 Danielsson, Keski-Vakkuri and Kruczenski 1) 2)

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

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. tdethermalization /tthermalization J is a turning point

18. tdethermalization /tthermalization Data: .A., I.Volovich,1211.6041

19. tdethermalization /tthermalization Data:

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

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

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

23. Kerr-ADS-BH Geometry Geodesics i B1,2 = (β1,2 − γ2)(β1,2 − γ1)

24. - Geodesics which start and finish at Turning point * Thermal geodesics a=0 V. Balasubramanian, A. Bernamonti, J. deBoer, N. Copland, B. Craps, E. Keski-Vakkuri, B. MullerandA. Schaferetal., 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 AdS5 Centrality dependence of thermalization time d=3 no dependence d>3 ? Anisotropy decreases thermalization time.