1. Holographic Description of Quark-Gluon Plasma Irina Aref'eva Steklov Mathematical Institute, RAN, Moscow JINR, Dubna March 19, 2014

2. Quark-Gluon Plasma Formation in Heavy Ion Collisions in Holographic Description JINR, Dubna April 3, 2013

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. Outlook (Last year) Quark-Gluon Plasma(QGP) in heavy-ions collisions(HIC) Holography description of QGP in equilibrium Holography description of formation of QGP in HIC Black Holes formation in AdS Thermalization time/Dethermalization time Non-central collisions in holography description

5. QGP in Heavy Ion Collision One of the fundamental questions in physics is: what happens to matter at extreme densities and temperatures as may have existed in the first microseconds after the Big Bang The aim of heavy-ion physics is to create such a state of matter in the laboratory. Evolution of a Heavy Ion Collision

6. 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

7. 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). The above observations, have 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 I.A. UFN, 2014

8. What we know Multiplicity Thermalization time Interquark potential Hard probes (transport coefficients drag force, jet quenching,…)

9. Multiplicity Plot from: ATLAS Collaboration 1108.6027

10. “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

11. AdS/CFT correspondence + requirement of regularity at horizon Gubser,Klebanov,Polyakov Witten, 1998 M=AdS

12. AdS/CFT Correspondence via Geodesics. Example I. D=2 x-x’=x-x’= AdS 3 x x’x’ Correlators with T=0 z0z0

13. Correlators with T via AdS/CFT Example II. D=2 BHAdS Bose gas Temperatute

14. Average of non-local operator with a contour on the boundary = action of a classical string ending on the contour AdS/CFT correspondence for non-local operator : is the singlet potential of interquark interaction

15. Maldacena hep-th/9803002

16. Sonneschein…hep-th/9803137; Rey, Yee…hep-th/9803135

17. BTZ –metricLorentz Euclidean (Banados,Teitelboim,Zanelli; 1992) (Banados,Teitelboim,Zanelli; 1992)

18. Classical string actions and parametrization Lorentz Euclidean

19. Potential: For some phi there is a string breaking!

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

21. Hologhraphic thermalization 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 Studies of BH formation in AdS D+1 Time of thermalization in HIC Multiplicity in HIC Profit:

22. colliding gravitational shock waves drop of a shell of matter ("null dust"), infalling shell geometry = Vaidya metric sudden perturbations of the metric near the boundary that propagate into the bulk Formation of BH in AdS. Deformations of AdS metric leading to BH formation Gubser, Pufu, Yarom, Phys.Rev., 2008 JHEP, 2009 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,….. IA,IVolovich, 2013; IA,Bagrov,Koshelev,2013 Chesler, Yaffe, PRL, 2011

23. Colliding gravitational shock waves AdS/CFT correspondence

24. Nucleus collision in AdS/CFT The metric of two shock waves in AdS corresponding to collision of two ultrarelativistic nucleus in 4D

26. Multiplicity: Hologhrapic formula vs experimental data Plot from: ATLAS Collaboration 1108.6027

27. The mininal black hole entropy can be estimated by trapped surface area We describe heavy-ion collisions by the wall-wall shock wave collisions in (or in its modification) S. Lin, E. Shuryak, 1011.1918 I. A., A. A. Bagrov and E. O. Pozdeeva,(2012)

28. We describe heavy-ion collisions by the wall-wall shock wave collisions in (or in its modification) S. Lin, E. Shuryak, 1011.1918 I. A., Bagrov and E.Pozdeeva,(2012) Shock wave metric modified by b-factor The Einstein equation for particle in dilaton field

29. Shock wave metric modified by b-factor The Einstein equation for particle in dilaton field I. A., E.Pozdeeva,T.Pozdeeva (2013,2014)

30. AdS space-time modifications For the standard AdS space-time b(z) factor has form b(z)=L/z b-factors in modify AdS space-time

31. Mixed factor a=1/2

32. Backup

33. Power-law wrapping factor S= The multiplicity of particles produced in HIC(PbPb-and AuAu-collisions) dependents as s 0.15 NN in the range 10-10 3 GeV Power-law b-factor coinsides with experimental data at a≈0.47

34. Dilaton potential

37. Thermalization Time Thermalization Time (via Vaidya) and Centricity Non-centricityKerr-ADS-BH I.A. A.Koshelev, A.Bagrov, JHEP, 013 D=3 D>3, in progress

38. Conclusion Formation of QGP of 4-dim QCD  Black Hole formation in AdS 5 Multiplicity: AdS-estimations fit experimental data Non-centricity decreases thermalization time. Drag forces (in progress),