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

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

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

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

5. Hologhraphic thermalization
Lecture II.: Hologhraphic Description of Formation of Quark Gluon
Plasma
Hologhraphic thermalization
Thermalization of
QFT in Minkowski
D-dim space-time
Black Hole formation
in Anti de Sitter
(D+1)-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
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
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
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. Deformations of AdS metric infalling shell (Vaidya metric) )
Balasubramanian
at all
3 measures of thermalization:
two-point functions,
Wilson loop v.e.v.,
entanglement entropy.
Estimations of thermalization times
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
CHECK ++, --
Two ultrarelativistic nucleus in D=4 correspond to the metric of two shock waves in AdS 15

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

17. 4-dim Aichelburg-Sexl shock waves to describe particles,
't Hooft and Amati, Ciafaloni and Veneziano
Aichelburg-Sexl shock waves to describe particles,
Shock Waves > BH
Colliding plane gravitation waves 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

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

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

20. Trapped Surface for two shock waves in AdSX+ 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. Multiplicity in HIC in D=4 can be estimated
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. D=4 Multiplicity = Area of trapped surface in D=5
Gubser, Pufu, Yarom, , Alvarez-Gaume, C. Gomez, Vera, Tavanfar, Vazquez-Mozo,
IA, Bagrov, Guseva,
Lattice calculations
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
dNch/dη ≈ 1600 ± 76 (syst)
≈ 30,000 particles in total, ≈ 400 times pp !
Energy density ε > 3 x RHIC (fixed τ0,)
Temperature + 30%
Modified
Hologhrapic
Model

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

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 27 27 27

28. Formation of trapped surfaces is only possible when Q<Qcr
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,
I.A., A.Bagrov, E.Pozdeeva,

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