Probing Out of E quilibrium Physics

1. Probing Out of Equilibrium Physics Nick Evans University of Southampton • D3/D7 and time dependent solutions • Thermalization • Finite T phase transitions • Quenches • Inflation

2. Can also apply to D3/D5 defect theory… Orthonormal, complete set of wave functions

3. Add Confinement &Chiral Symmetry Breaking Dilaton Flow Geometry: Gubser, Sfetsos BEEGK, Ghoroku.. B field enters the DBI action as a dilaton profile – causes chiral symmetry breaking but not confinement.

4. Thermalizing N=2 Meson Clouds Time dependent problems for the probe are simple and the ODEs solvable in egMathematica Das, Nishioka , Takayanagi In linearized approx.. We can fill space with a cloud of non-interacting mesons… UV IR

5. For small amplitude interacting solution.. at early times we see classic perturbation theory mixing between states Leave for long enough and presumably, time averaged, the energy per mode will look Boltzmanexp(-m/kT)…. Mesons thermalize but do they dissolve into quark plasma? Is the formation of a world-sheet zero in g_tt an horizon and hence thermalization?

6. A full solution at large amplitude: Horizons come, horizons go… Could the initial condition have contained overlap with a thermal state at line one? To form a static or growing horizon we must have back-reaction….

7. Phase Transitions in Gapped Systems Eg B+T D3/D7 system Johnson, Filev Horizon grows and eats D7 - first order phase transition… To watch this transition in real time we use Janik’s time dependent solution for a cooling/warming fireball…

8. Expectations of First Order Transition NE, Kalaydzhyan, Kim, Kirsch 10.11.2519 Transition proceeds by bubble nucleation….

10. Quenches in Gapped Systems NE, French, Kim 1009.5678 , We can also change B at fixed T… Rolls and over shoots At finite T the additional physics emerges when the D7 hits the horizon… the mesonic spectrum becomes quasi-normal and there is energy loss CfBhaseen, Gauntlett , Simons, Julian Sonner, Wiseman

11. We have identified five behaviours No change after quench… Oscillation away from black hole Oscillation onto black hole either on a) first pass onto black hole b) After multiple passes over black hole Oscillation onto black hole, loosing energy and ending in oscillatory phase just above horizon…

12. Currently mapping out phase diagram (with Jon Shock, Keun-Young Kim)

13. Composite Inflatons NE, French, Kim 1009.5678 ,1208.3060 The simple quench from B=0 to B none zero is an inflation roll… How can we extend this roll? This would replace the unnatural scalar in inflation models with a strongly coupled gauge theory… ie a composite inflaton… We need…

14. Walking Dynamics Such theories probably exist … Cf Banks Zak Seiberg N=1 SUSY duality Such theories have enhanced UV quark condensate Constructing gravity duals of such theories is hard work.. (cfKiritsis, Jarvinen.. Nunez, Piai… )… What does a probe D7 see in a deformed AdS background?

15. Effective Probe Dynamics Alvares, NE, Kim 1204.2474 The mass is just a statement of the running of the dimension of qq The instability is due to a violation of the BF bound

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17. The roll from false vacuum to true… The meson masses of the unstable vacuum.. There is a single inflaton… whose mass falls to zero as one approaches the transition… You can also time the roll in an explicit time dependent computation and show it increases in time as one approaches the CW transition… If you’re willing to fine tune to the transition you can get an arbitrarily flat potential/ long roll time…

18. Summary • Probe branes provide a computational simple way to study non-equilibrium problems • Meson thermalization is present but not breakdown into a quark plasma • Real time computations through gap-no gap phase transitions are possible • Expected features of a quench are present - oscillations damped by energy loss to quasi-normal modes • Can compute when strongly coupled physics contributes to cosmology now - walking dynamics seems linked to inflation…