Holographic Thermal Flow: Modeling Collisions and Thermalization

1. Inhomogeneous thermalization and strongly coupled thermal flow via holography Daniel Fernández Max Planck InstituteforPhysicsin Munich Iberian Strings 2016 - Madrid IFT

2. Quark-gluon plasma thermalization[Chesler, Yaffe, Heller, Romatschke, Mateos, vd Schee, Bantilan] • Turbulence in Gravity[Lehner, Green, Yang, Zimmerman, Chesler, Adams, Liu] • Drivensuperconductors[Rangamani, Rozali, Wong] • Quantum quenches[Balasubramanian, Buchel, Myers, van Niekerk, Das] • Revivals[Mas, Lopez, Serantes, da Silva] Time-dependent Holography 1 2 Collisions modeled as shockwaves Thermal flow modeled as dynamical horizon 1/14

3. Part 1:Heavy Ion Collisions

4. Conservation Law: • Slow evolution of expectation values. • Assumption: local quasi-equilibrium. Hydrodynamics approach Gradient expansion: Include viscosity term: 1st and higher order gradient terms In HICs, the kind of physics that dominates is viscous fluid dynamics. Connection to holography: • Condition to work: small gradients. • But good description of HIC data! [Luzum, Romatschke ‘09] 2/14

5. (Picture not to scale) Out of equilibrium • Non-hydro degrees of freedom are dominant. • Gravitational model: Shock wave collisions. Evolution of a Heavy Ion Collision Hydrodynamization • Transition to the hydrodynamics approximation. Thermalization • Isotropy of the diagonal components of Tmn in local rest frame. Hadronization • Kinetic theory is applicable. 3/14

6. Ansatz: Boundary EOM: Gravitational formulation Generalize Simplification from 3+1 to 2+1 by: Alternative: Use polar coordinates. Assuming boost invariance and breaking rotational symmetry, 4/14

7. AH EH Gaussian shocks null geodesics • Two separated shocks with finite thickness and energy density, moving toward each other: t Initial Condition Exact analytic solution, in Fefferman-Graham coordinates. is the bdry. energy density, arbitrary if r Choice: Characteristic Formulation (Generalize for perturbations) • Ingoing Eddington-Finkelstein coordinates. • Foliation of null hypersurfaces. • IR cutoff → require fixed-r Apparent Horizon condition. [Winicour ’01, Chesler, Yaffe ‘08] 5/14

8. Energy density: Stress-Energy Tensor results • The inhomogeneities are evolved on top of the dynamical background: 6/14

9. Compare with hydro results Mid-rapidity Comparing with hydrodynamics • Dramatic rise in the pressures. • Very anisotropic and out-of-eq. • Hydro holds almost from the beginning. [Chesler, Yaffe ‘10] Isotropization time and hydrodynamization time are completely different. [Fernández ’15] 7/14

10. Outlook: Chiral Magnetic Effect In relativistic chiral plasma, the anomaly is present: In a Heavy Ion Collision: → Anomalous electric current: • Strong magnetic fields are produced by the charged “spectators” ( ) • Anomalous electric currents → Observable effects in hadron production. Holomodel ingredients • Massive → Emulate dynamical gluons for . • Scalar field → Recover gauge invariance. • CS term → Non-dynamical part of anomaly. [Rebhan, Schmitt, Stricker'09] [Gürsoy, Kharzeev, Rajagopal ’14] [Jiménez-Alba, Landsteiner, Melgar ‘15] • Stückelberg-Chern-Simons theory: …evolution of axial charge? 8/14

11. Part 2:Thermal Flow

12. [Bernard, Doyon ’12] Thermal quench in 1+1 Two exact copies initially at equilibrium, independently thermalized. Universal regime of thermal transport Conservation eqs & tracelessness: NOPE Expectation for CFT: shock waves emanating from interface, converge to non-equilibrium Steady State. 9/14

13. [Bhaseen, Doyon, Lucas, Schalm ’13] Generalization to any d • Assume ctant. homogeneous heat flow as well: Thermal transport in d>1 • Generic d prediction • Effectivedimensionreduction to 1+1. • Linear response regime: • → Hydroeqs. explicitlysolvable. Final steady state characterized by where Long time limit 10/14

14. Heat transport dominated by diffusion instead of flow? • Shockwave velocities: II III I Hydrodynamics approach Hydrodynamical evolution of 3 regions Match solutions ↔ Asymptotics of the central region with Two configurations: - Thermodynamic branch- “second branch” [Bhaseen, Doyon, Lucas, Schalm ’13] [Chang, Karch, Yarom’13] 11/14

15. [Amado, Yarom ’15] Energy transport: Lorentz-boosted thermal distribution → Expectation: Boosted black brane Holographic approach Gravitational problem: Full out-of-equilibrium evolution of Einstein’s equations. Ansatz: Energy flux Energy density 12/14

16. How does information get exchanged between the systems which are isolated at t=0? • Entanglement entropy • → Holographic measure: • Regularization: Substract result at T=0: Information Flow y x z 13/14

17. Entanglement Entropies Mutual Information What do we learn about A by looking at B? • Shockwaves transport information. • M.I. grows as shocks pass through the region. B A Ac Ac A [Erdmenger, Fernández, Flory, Megías, Straub ’15] 14/14

18. Thank you for your attention