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

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

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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.

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

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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 Boltzman exp(-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?

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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….

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Phase Transitions in Gapped Systems Eg B+T D3/D7 system 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… Johnson, Filev

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

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Quenches in Gapped Systems 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 NE, French, Kim 1009.5678, Cf Bhaseen, Gauntlett, Simons, Julian Sonner, Wiseman

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Oscillation away from black hole We have identified five behaviours 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… No change after quench…

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

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Composite Inflatons 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… NE, French, Kim 1009.5678,1208.3060

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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.. (cf Kiritsis, Jarvinen.. Nunez, Piai… )… What does a probe D7 see in a deformed AdS background?

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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 Effective Probe Dynamics Alvares, NE, Kim 1204.2474

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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…

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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…

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