1. “Understanding confinement”, May 16-21, 2005 Quantum Black Holes, Strong Fields, and Relativistic Heavy Ions D. Kharzeev

2. Outline • Black holes and accelerating observers • Event horizons and pair creation in strong fields • Thermalization and phase transitions in relativistic nuclear collisions DK, K. Tuchin, hep-ph/0501234

3. Black holes radiate S.Hawking ‘74 Black holes emit thermal radiation with temperature acceleration of gravity at the surface

4. Similar things happen in non-inertial frames Einstein’s Equivalence Principle: Gravity Acceleration in a non-inertial frame An observer moving with an acceleration a detects a thermal radiation with temperature W.Unruh ‘76

5. In both cases the radiation is due to the presence of event horizon Black hole: the interior is hidden from an outside observer; Schwarzschild metric Accelerated frame: part of space-time is hidden (causally disconnected) from an accelerating observer; Rindler metric

6. From pure to mixed states:the event horizons mixed state pure state mixed state pure state

7. Thermal radiation can be understood as a consequence of tunneling through the event horizon Let us start with relativistic classical mechanics: velocity of a particle moving with an acceleration a classical action: it has an imaginary part…

8. well, now we need some quantum mechanics, too: The rate of tunneling under the potential barrier: This is a Boltzmann factor with

9. Accelerating detector • Positive frequency Green’s function (m=0): • Along an inertial trajectory • Along a uniformly accelerated trajectory Unruh,76 Accelerated detector is effectively immersed into a heat bath at temperatureTU=a/2

10. An example: electric field The force: The acceleration: The rate: What is this? Schwinger formula for the rate of pair production; an exact non-perturbative QED result factor of 2: contribution from the field

11. + … + + The Schwinger formula e- E e+ Dirac sea

12. The Schwinger formula • Consider motion of a charged particle in a constant electric field E. Action is given by Equations of motion yield the trajectory wherea=eE/mis the acceleration Classically forbidden trajectory

13. Action along the classical trajectory: • In Quantum Mechanics S(t) is an analytical function of t • Classically forbidden paths contribute to • Vacuum decays with probability Sauter,31 Weisskopf,36 Schwinger,51 • Note, this expression can not be expanded in powers • of the coupling - non-perturbative QED!

14. Pair production by a pulse E Consider a time dependent field t • Constant field limit • Short pulse limit a thermal spectrum with

15. Chromo-electric field:Wong equations • Classical motion of a particle in the external non-Abelian field: The constant chromo-electric field is described by Solution: vector I3 precesses about 3-axis with I3=const Effective Lagrangian:Brown, Duff, 75; Batalin, Matinian,Savvidy,77

16. An accelerated observer consider an observer with internal degrees of freedom; for energy levels E1 and E2 the ratio of occupancy factors Bell, Leinaas: depolarization in accelerators? For the excitations with transverse momentum pT:

17. but this is all purely academic (?) Can one study the Hawking radiation on Earth? Gravity? Take g = 9.8 m/s2; the temperature is only

18. Electric fields? Lasers? compilation by A.Ringwald

19. Condensed matter black holes? Unruh ‘81; e.g. T. Vachaspati, cond-mat/0404480 “slow light”?

20. Hagedorn temperature! Strong interactions? Consider a dissociation of a high energy hadron of mass m into a final hadronic state of mass M; The probability of transition:m M Transition amplitude: In dual resonance model: b=1/2 universal slope Unitarity:P(mM)=const, limiting acceleration

21. Fermi - Landau statistical model of multi-particle production Hadron production at high energies is driven by statistical mechanics; universal temperature Lev D. Landau 1908-1968 Enrico Fermi 1901-1954

22. Where on Earth can one achieve the largest acceleration (deceleration) ? Relativistic heavy ion collisions! - stronger color fields:

23. Strong color fields (Color Glass Condensate) as a necessary condition for the formation of Quark-Gluon Plasma The critical acceleration (or the Hagedorn temperature) can be exceeded only if the density of partonic states changes accordingly; this means that the average transverse momentum of partons should grow CGC QGP

24. Quantum thermal radiation at RHIC The event horizon emerges due to the fast decceleration of the colliding nuclei in strong color fields; Tunneling through the event horizon leads to the thermal spectrum Rindler and Minkowski spaces

25. The emerging picture Big question: How does the produced matter thermalize so fast? Perturbation theory + Kinetic equations

26. Fast thermalization horizons Rindler coordinates: collision point Qs Gluons tunneling through the event horizons have thermal distribution. They get on mass-shell int=2Qs (period of Euclidean motion)

27. Deceleration-induced phase transitions? • Consider Nambu-Jona-Lasinio model in Rindler space • Commutation relations: • Rindler space: e.g., Ohsaku ’04

28. Gap equation in an accelerated frame • Introduce the scalar and pseudo-scalar fields • Effective action (at large N): • Gap equation: where

29. Rapid deceleration induces phase transitions Nambu- Jona-Lasinio model (BCS - type) Similar to phenomena in the vicinity of a large black hole: Rindler space Schwarzschild metric

30. Black holes A link between General Relativity and QCD? solution to some of the RHIC puzzles? RHIC collisions