Holographic description of heavy-ions collisions

1. Lecture I: Holographic description of Quark Gluon Plasma (QGP in equilibrium) Holographic description of heavy-ions collisions Lecture II: Holographic Description of Formationof Quark Gluon Plasma. Multiplicity Irina Aref’eva SteklovMathematicalInstitute, Moscow 7th MATHEMATICAL PHYSICS MEETING:Summer School and Conference on Modern Mathematical Physics 9 - 19 September 2012, Belgrade, Serbia

2. Lecture I. : Hologhraphic description of Quark GluonPlasma (QGP in equilibruum) Holography for thermal states Black hole in AdSD+1-space-time = TQFT in MD-space-time TQFT = QFT with temperature

3. AdS/CFT correspondence in Euclidean space. T=0 FROM Lecture 1 denotes Euclidean time ordering + requirement of regularity at horizon g:

4. FROM Lecture 1 -- retarded temperature Green function in 4-dim Minkowski AdS/CFT correspondence. Minkowski. T=0 QFT at finite temperature (D=4) Classical gravity with black hole (D=5) Son, Starinets, 2002 F -- kernel of the action for the (scalar) field in AdS5 with BLACK HOLE LHS QFT with T Bogoliubov-Tyablikov Green function

5. Lecture II.: Hologhraphic Description of Formation of Quark Gluon Plasma Hologhraphic thermalization Black Hole formation in Anti de Sitter (D+1)-dim space-time Thermalization of QFT in Minkowski D-dim space-time Time of thermalization in HIC Studies of BH formation in AdSD+1 Multiplicity in HIC HIC = heavy ions collisions

6. Formation of BH in AdS. Deformations of AdS metric leading to BH formation Gubser, Pufu, Yarom, Phys.Rev. , 2008 Alvarez-Gaume, C. Gomez, Vera, Tavanfar, Vazquez-Mozo, PRL, 2009 IA, Bagrov, Guseva, Joukowskaya, 2009 JHEP Kiritsis, Taliotis, 2011 • 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 Danielsson, Keski-Vakkuri and Kruczenski ……. Chesler, Yaffe, 2009

7. Deformations of MD metric by infalling shell Vaidya 1951 4-dimensional infalling shell geometry (Vaidya metric) flat

8. Deformations of MD metric by infalling shell 4-dimensional Minkowski. Penrose diagram

9. Deformations of MD metric by infalling shell .Vaidya metric =

10. 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)

11. Estimations of thermalization times Deformations of AdS metric infalling shell (Vaidya metric) ) Balasubramanian at all1103.2683 3 measures of thermalization: two-point functions, Wilson loop v.e.v., entanglement entropy. Hawking temperature (in 5) = temperature of GQP (in 4)

12. Geodesics and correlators

13. Geodesics and correlators

14. Dual description of ultrarelativistic nucleus by shock waves An ultrarelativistic nucleus is a shock wave in 4d with the energy-momentum tensor Woods-Saxon profile The metric of a shock wave in AdS corresponding to the ultrarelativistic nucleus in 4d is Janik, Peschanksi ‘05

15. Dual description of collision of 2 ultrarelativistic nucleus Two ultrarelativistic nucleus in D=4 correspond to the metric of two shock waves in AdS

16. Dual description of collision of 2 ultrarelativistic nucleus Question: what happens in AdS after collision of two shock waves?

17. 't Hooft and Amati, Ciafaloni and Veneziano 1987 Aichelburg-Sexl shock waves to describe particles, Shock Waves ------ > BH Collidingplanegravitationwaves to describe particles Plane Gravitational Waves ----- > BH I.A., Viswanathan, I.Volovich, Nucl.Phys., 1995 Boson stars (solitons) to describe particles M.Choptuik and F.Pretorius, PRL, 2010 4-dim

18. BLACK HOLE FORMATION =Trapped Surface(TS) • Theorem (Penrose): BH Formation = TS

19. Point sourced shock waves p The chordal coordinate Different profiles An arbitrary gravitational shock wave in AdS5

20. Trapped Surface for two shock waves in AdS AdS3 X+ X- X TS comprises two halves, which are matched along a “curve”

21. Trapped Surface (TS) for two shock waves in AdS • Theorem. TS for two shock waves = . solution to the following Dirichlet problem Eardley, Giddings; Kang, Nastase,….

22. Conjecture Multiplicity in HIC in D=4 can be estimated by the area of TS in AdS5 formed in collision of shock waves Gubser, Pufu, Yarom

23. Lattice calculations D=4 Multiplicity = Area of trapped surface in D=5 Gubser, Pufu, Yarom, 0805.1551, Alvarez-Gaume, C. Gomez, Vera, Tavanfar, Vazquez-Mozo, 0811.3969 IA, Bagrov, Guseva, 0905.1087 Hawking-Page relation From a Woods-Saxon profile for the nuclear density

24. Multiplicity: Experimental data, Landau, AdS-estimation Phenomenological estimation: total multiplicity and the number of charged particle

25. Multiplicity: Landau’s/Hologhrapic formula vs experimental data Landau’s formula Plots from: Alice Collaboration PRL, 2010 ATLAS Collaboration 1108.6027 Modified Hologhrapic Model

26. Cai, Ji, Soh, gr-qc/9801097 IA, 0912.5481 • Dilaton shock waves Kiritsis, Taliotis, 1111.1931 Multiplicity very closed to LHC data Different profiles different multiplicities Goal: try to find a profile to fit experimental data Cut-off Gubser, Pufu, Yarom,II

27. Wall-on-wall dual modelof heavy-ion collisions • Plane shock waves The Einstein equation Lin, Shuryak, 09 Wu, Romatschke, Chesler, Yaffe, Kovchegov,…. • Simplify calculation • But strictly speaking not correct • One needs a regularization I.A., A.Bagrov, E.Pozdeeva, JHEP, 2012

28. Phase diagram from dual approach Formation of trapped surfaces is only possible when Q<Qcr Red for smeared matter Blue for point-like I.A., A.Bagrov, Joukovskaya, 0909.1294 I.A., A.Bagrov, E.Pozdeeva, 1201.6542

29. Conclusion Black Hole in AdS5 QGP in 4-dim 2001-2011 Black Hole formation in AdS5 formation of QGP of 4-dim QCD • Formula for multiplicity 2008-2012 • Future directions: • multiplicity and quark potential for the same dual gravity model • New phase transitions related with parameters of gravity models