Heavy Quark Diffusion in AdS/CFT

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1 Purdue University January 5th 2011

2 AdS/CFT is a correspondence that relates certain Quantum Field Theories and certain String Theories.

3 Some characteristics of the correspondence. Large N c N = 4 SYM theory in four dimensions is equivalent to type IIB string theory on AdS 5 S 5.

4 Some characteristics of the correspondence. Large N c N = 4 SYM theory in four dimensions is equivalent to type IIB string theory on AdS 5 S 5. λ t Hooft R4 α 2, Large λ t Hooft limit IIB supergravity

5 Some characteristics of the correspondence. Large N c N = 4 SYM theory in four dimensions is equivalent to type IIB string theory on AdS 5 S 5. λ t Hooft R4 λ 4πN c, Large α 2 λ t Hooft limit IIB supergravity g s, Beyond the planar limit stringy loops.

6 Some characteristics of the correspondence. Large N c N = 4 SYM theory in four dimensions is equivalent to type IIB string theory on AdS 5 S 5. λ t Hooft R4 λ 4πN c, Large α 2 λ t Hooft limit IIB supergravity g s, Beyond the planar limit stringy loops. g µν (x, z 0) T µν

7 Some characteristics of the correspondence. Large N c N = 4 SYM theory in four dimensions is equivalent to type IIB string theory on AdS 5 S 5. λ t Hooft R4 λ 4πN c, Large α 2 λ t Hooft limit IIB supergravity g s, Beyond the planar limit stringy loops. g µν (x, z 0) T µν φ(x, z 0) Tr[F 2 + susy]

8 Some characteristics of the correspondence. Large N c N = 4 SYM theory in four dimensions is equivalent to type IIB string theory on AdS 5 S 5. λ t Hooft R4 λ 4πN c, Large α 2 λ t Hooft limit IIB supergravity g s, Beyond the planar limit stringy loops. g µν (x, z 0) T µν φ(x, z 0) Tr[F 2 + susy] Fundamental string quark.

9 Some characteristics of the correspondence. Large N c N = 4 SYM theory in four dimensions is equivalent to type IIB string theory on AdS 5 S 5. λ t Hooft R4 λ 4πN c, Large α 2 λ t Hooft limit IIB supergravity g s, Beyond the planar limit stringy loops. g µν (x, z 0) T µν φ(x, z 0) Tr[F 2 + susy] Fundamental string quark. A thermal state in the CFT Black hole in AdS.

10 Some characteristics of the correspondence. Large N c N = 4 SYM theory in four dimensions is equivalent to type IIB string theory on AdS 5 S 5. λ t Hooft R4 λ 4πN c, Large α 2 λ t Hooft limit IIB supergravity g s, Beyond the planar limit stringy loops. g µν (x, z 0) T µν φ(x, z 0) Tr[F 2 + susy] Fundamental string quark. A thermal state in the CFT Black hole in AdS. We can think of AdS/CFT as a tool to compute interesting quantities in field theory.

11 Comparing N = 4 SYM with QCD? No confinement. Coupling doesn t run: it s a parameter you can dial.

12 Comparing N = 4 SYM with QCD? No confinement. Coupling doesn t run: it s a parameter you can dial. No chiral condensate.

13 Comparing N = 4 SYM with QCD? No confinement. Coupling doesn t run: it s a parameter you can dial. No chiral condensate. All fundamental matter fields are in adjoint representation: A µ, four Majorana fermions λ i, six real scalars X I.

14 Comparing N = 4 SYM with QCD? No confinement. Coupling doesn t run: it s a parameter you can dial. No chiral condensate. All fundamental matter fields are in adjoint representation: A µ, four Majorana fermions λ i, six real scalars X I. Many phenomenological models (AdS/QCD) improve on the previous points.

15 We wish to describe a hard heavy external quark We model the heavy quark by the end of a moving string. (Gubser:2006)

16 We wish to describe a hard heavy external quark We model the heavy quark by the end of a moving string. (Gubser:2006) We impose boundary conditions on the boundary of AdS for the string.

17 We wish to describe a hard heavy external quark We model the heavy quark by the end of a moving string. (Gubser:2006) We impose boundary conditions on the boundary of AdS for the string. The quark moves at a constant speed with energy provided by an external force.

18 R 3,1 measure momentum flow across horizon momentum flow I ξ(y) q v The drag force is computed by measuring the momentum flux down the string. The position of I is arbitrary because the energy-momentum current is conserved.

19 R 3,1 T mn q v AdS Schwarzschild 5 horizon h mn fundamental string In blue: the trailing string of an external quark, following. The dashed line shows classical propagation of a graviton from the string to the boundary, where its behavior can be translated into the stress-energy tensor T mn of the boundary gauge theory.

20 The drag force is found to be:

21 The drag force is found to be: F = π 2 λt 2 v 1 v 2 = p τ,

22 The drag force is found to be: F = π 2 λt 2 v 1 v 2 = p τ, and the diffusion time

23 The drag force is found to be: F = π 2 λt 2 v 1 v 2 = p τ, and the diffusion time τ = 2Mq π. λt 2

24 The drag force is found to be: F = π 2 λt 2 v 1 v 2 = p τ, and the diffusion time τ = 2Mq π. λt 2 τ charm 2fm, τ bottom 6fm, for T = 250MeV.

25 Similarly we can calculate the jet quenching parameter ˆq from a Wilson loop (Liu, Rajagopal, Wiedemann:2006)

26 Similarly we can calculate the jet quenching parameter ˆq from a Wilson loop (Liu, Rajagopal, Wiedemann:2006) W e ˆqL L 2

27 Similarly we can calculate the jet quenching parameter ˆq from a Wilson loop (Liu, Rajagopal, Wiedemann:2006) W e ˆqL L 2 For N = 4 we find ˆq = Γ[3/4] Γ[5/4] 2λπ 3/2 T 3.

28 Similarly we can calculate the jet quenching parameter ˆq from a Wilson loop (Liu, Rajagopal, Wiedemann:2006) W e ˆqL L 2 For N = 4 we find ˆq = Γ[3/4] Γ[5/4] 2λπ 3/2 T 3. For λ = 5.5 and T = 250MeV, ˆq = 2GeV 2 /fm.

29 Some properties of the model Thermal transport and drag in this model We would like to describe QCD in a holographic setting. U.Gursoy, E.Kiritsis, L.Mazzanti, F.Nitti, G.M. A new string inspired phenomenological model.

30 Some properties of the model Thermal transport and drag in this model We would like to describe QCD in a holographic setting. U.Gursoy, E.Kiritsis, L.Mazzanti, F.Nitti, G.M. A new string inspired phenomenological model. A running constant is introduced via the dilaton in five dimensions.

31 Some properties of the model Thermal transport and drag in this model We would like to describe QCD in a holographic setting. U.Gursoy, E.Kiritsis, L.Mazzanti, F.Nitti, G.M. A new string inspired phenomenological model. A running constant is introduced via the dilaton in five dimensions. Similar approach to the hard wall and soft wall models.

32 Some properties of the model Thermal transport and drag in this model We would like to describe QCD in a holographic setting. U.Gursoy, E.Kiritsis, L.Mazzanti, F.Nitti, G.M. A new string inspired phenomenological model. A running constant is introduced via the dilaton in five dimensions. Similar approach to the hard wall and soft wall models. The model consists of gravity plus a scalar in five dimensions.

33 Some properties of the model Thermal transport and drag in this model Some properties of the model. The terms of the dilaton potential are determined by requiring:

34 Some properties of the model Thermal transport and drag in this model Some properties of the model. The terms of the dilaton potential are determined by requiring: Asymptotic freedom close to the boundary.

35 Some properties of the model Thermal transport and drag in this model Some properties of the model. The terms of the dilaton potential are determined by requiring: Asymptotic freedom close to the boundary. Matching the spectrum of the glueballs with the lattice.

36 Some properties of the model Thermal transport and drag in this model Some properties of the model. The terms of the dilaton potential are determined by requiring: Asymptotic freedom close to the boundary. Matching the spectrum of the glueballs with the lattice. Matching thermodynamics with lattice for high temperatures.

37 Some properties of the model Thermal transport and drag in this model Some properties of the model. The terms of the dilaton potential are determined by requiring: Asymptotic freedom close to the boundary. Matching the spectrum of the glueballs with the lattice. Matching thermodynamics with lattice for high temperatures. These conditions give a first order transition - Hawking Page between the confined and the deconfined phase at T C 250MeV.

38 Some properties of the model Thermal transport and drag in this model Some thermodynamical quantities for the new model The entropy and energy density and pressure for ihqcd. The points come from lattice results.

39 Some properties of the model Thermal transport and drag in this model Some thermodynamical quantities for the new model The conformal anomaly and the speed of sound for ihqcd. The points come from lattice results.

40 Some properties of the model Thermal transport and drag in this model Drag force in ihqcd F Fc T Tc 1.01 T Tc 1.48 T Tc 1.99 T Tc v The ratio of the drag force in ihqcd to the conformal N = 4 SYM case is shown. For high velocities and high temperatures asymptotic freedom becomes important. For N = 4 SYM the t Hooft coupling is chosen to be 6.

41 Some properties of the model Thermal transport and drag in this model Drag force in ihqcd F Fc T Tc v 1 10 v 4 10 v 7 10 v 9 10 The ratio of the drag force in ihqcd to the conformal N = 4 SYM case is shown. For high velocities and high temperatures asymptotic freedom becomes important. For N = 4 SYM the t Hooft coupling is chosen to be 6.

42 Some properties of the model Thermal transport and drag in this model Diffusion in ihqcd Τ fm 7 6 Charm 5 T c T c 2 2 T c T c E MeV Diffusion time for the Charm quark, as a function of energy, for different ratios of the temperature to the IHQCD transition temperature Tc.

43 Some properties of the model Thermal transport and drag in this model T, MeV T equiv. T equiv /T C τ diff Charm τ diff Bottom fm 8.64 fm fm 7.04 fm fm 6.09 fm fm 5.31 fm fm 3.51 fm fm 2.56 fm Table: In this table the diffusion times for the charm and a bottom quark are shown. Diffusion times have been evaluated at an energy of E = 3 M q and at the equivalent temperature of the alternative scheme, shown in the third column.

44 Some properties of the model Thermal transport and drag in this model Jet Quenching in ihqcd q ihqcd q conf T Tc

45 Some properties of the model Thermal transport and drag in this model Conclusions AdS/CFT provides us with tools to study strongly coupled plasmas.

46 Some properties of the model Thermal transport and drag in this model Conclusions AdS/CFT provides us with tools to study strongly coupled plasmas. It can also address questions of dynamics!

47 Some properties of the model Thermal transport and drag in this model Conclusions AdS/CFT provides us with tools to study strongly coupled plasmas. It can also address questions of dynamics! Many topics not covered in this talk:

48 Some properties of the model Thermal transport and drag in this model Conclusions AdS/CFT provides us with tools to study strongly coupled plasmas. It can also address questions of dynamics! Many topics not covered in this talk: Langevin dynamics, quarkonium melting, conical emission, Mach cone...

49 Some properties of the model Thermal transport and drag in this model Conclusions AdS/CFT provides us with tools to study strongly coupled plasmas. It can also address questions of dynamics! Many topics not covered in this talk: Langevin dynamics, quarkonium melting, conical emission, Mach cone... Recent review arxiv: