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 9 - 19 September 2012, Belgrade, Serbia

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

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

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

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

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

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

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

Deformations of MD metric by infalling shell . Vaidya metric =

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)

Deformations of AdS metric infalling shell (Vaidya metric) ) Balasubramanian at all 1103.2683 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)

Geodesics and correlators

Geodesics and correlators

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

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

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

4-dim Aichelburg-Sexl shock waves to describe particles, 't Hooft and Amati, Ciafaloni and Veneziano 1987 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

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

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

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

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,….

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

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 Lattice calculations Hawking-Page relation From a Woods-Saxon profile for the nuclear density

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

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

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

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

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, 0909.1294 I.A., A.Bagrov, E.Pozdeeva, 1201.6542

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